Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield

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Edited by Andreas Seidel-Morgenstern

Membrane Reactors Distributing Reactants to Improve Selectivity and Yield

Edited by Andreas Seidel-Morgenstern Membrane Reactors

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Edited by Andreas Seidel-Morgenstern

Membrane Reactors Distributing Reactants to Improve Selectivity and Yield

The Editor Andreas Seidel-Morgenstern Otto-von-Guericke-Universität Institut für Verfahrenstechnik Universitätsplatz 2 39106 Magdeburg Germany and Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliograﬁe; detailed bibliographic data are available on the Internet at . © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microﬁlm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not speciﬁcally marked as such, are not to be considered unprotected by law. Composition Toppan Best-set Premedia Limited, Hong Kong Printing and Binding betz-druck GmbH, Darmstadt Cover Design Schulz Graﬁk-Design, Fußgönheim Printed in the Federal Republic of Germany Printed on acid-free paper ISBN: 978-3-527-32039-4

V

Contents Preface XI List of Contributors XV

1

1.1 1.2 1.3 1.4 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.6 1.6.1 1.6.2 1.7 1.8

2 2.1 2.2 2.3 2.3.1

Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors 1 Sascha Thomas, Christof Hamel, and Andreas Seidel-Morgenstern Challenges in Chemical Reaction Engineering 1 Concepts of Membrane Reactors 3 Available Membranes 6 Illustration of the Selectivity Problem 8 Reaction Rate, Conversion, Selectivity and Yield 9 Reaction Rates 9 Conversion 10 Mass Balance of a Plug Flow Tubular Reactor 10 Selectivity and Yield 12 Distributed Dosing in Packed-Bed and Membrane Reactors 13 Adjusting Local Concentrations to Enhance Selectivities 15 Optimization of Dosing Proﬁles 16 Kinetic Compatibility in Membrane Reactors 21 Current Status of Membrane Reactors of the Distributor Type 22 Notation used in this Chapter 23 Greek Symbols 23 Superscripts and Subscripts 23 Abbreviations 24 References 24 Modeling of Membrane Reactors 29 Michael Mangold, Jürgen Schmidt, Lutz Tobiska, and Evangelos Tsotsas Introduction 29 Momentum, Mass and Heat Balances 29 Transport Kinetics 35 Fluid-Filled Regions 35

Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

VI

Contents

2.3.1.1 2.3.1.2 2.3.1.3 2.3.2 2.3.2.1 2.3.2.2 2.3.2.3 2.3.2.4 2.4 2.5 2.6 2.6.1 2.6.2 2.6.3 2.7

Molecular Transport of Momentum 35 Heat Conduction 35 Molecular Diffusion 36 Porous Domains 38 Molecular Diffusion 39 Knudsen Diffusion 39 Viscous Flow 40 Models for Description of Gas Phase Transport in Porous Media 40 Reduced Models 42 Solvability, Discretization Methods and Fast Solution 44 Implementation in FLUENT, MooNMD, COMSOL and ProMoT 49 Application of FLUENT 49 Application of MooNMD 50 Application of ProMoT 51 Conclusion 56 Notation used in this Chapter 56 Latin Notation 56 Greek Notation 57 Super- and Subscripts 58 References 59

3

Catalysis and Reaction Kinetics of a Model Reaction 63 Frank Klose, Milind Joshi, Tanya Wolff, Henning Haida, Andreas SeidelMorgenstern, Yuri Suchorski, and H. Weiß Introduction 63 The Reaction Network of the Oxidative Dehydrogenation of Ethane 65 Catalysts and Structure–Activity Relations 66 Catalyst Preparation and Characterization 69 Mechanistic Aspects: Correlation Between Structure and Activity 71 Derivation of a Kinetic Model 73 Experimental 74 Catalyst 74 Set-Up 74 Procedures 75 Qualitative Trends 76 Overall Catalyst Performance 76 Evaluation of Intraparticle Mass Transfer Limitations 77 Quantitative Evaluation 78 Simpliﬁed Reactor Model and Data Analysis 78 Kinetic Models 78 Parameter Estimation 79 Suggested Simpliﬁed Model 79 Special Notation not Mentioned in Chapter 2 82 Latin Notation 82 Greek Notation 82 References 82

3.1 3.2 3.3 3.3.1 3.3.2 3.4 3.4.1 3.4.1.1 3.4.1.2 3.4.1.3 3.4.2 3.4.2.1 3.4.2.2 3.4.3 3.4.3.1 3.4.3.2 3.4.3.3 3.4.4

Contents

4

4.1 4.2 4.3 4.4 4.4.1 4.4.1.1 4.4.1.2 4.4.1.3 4.4.2 4.4.2.1 4.4.2.2 4.4.2.3 4.4.3 4.5 4.6 4.6.1 4.6.2 4.6.3 4.7

5

5.1 5.2 5.2.1 5.2.2 5.2.2.1 5.2.2.2 5.2.2.3 5.3 5.3.1 5.3.2 5.4 5.4.1 5.4.2

Transport Phenomena in Porous Membranes and Membrane Reactors 85 Katya Georgieva-Angelova, Velislava Edreva, Arshad Hussain, Piotr Skrzypacz, Lutz Tobiska, Andreas Seidel-Morgenstern, Evangelos Tsotsas, and Jürgen Schmidt Introduction 85 Aspects of Discretizing Convection-Diffusion Equations 87 Velocity Fields in Membrane Reactors 89 Determination of Transport Coefﬁcients and Validation of Models 97 Mass Transport Parameters of Multilayer Ceramic Membranes – Precursors Available 97 Task and Tools 97 Identiﬁcation by Single Gas Permeation 100 Validation by Isobaric Diffusion and by Transient Diffusion 105 Mass Transport Parameters of Metallic Membranes – Precursors not Available 107 Diagnosis 107 Identiﬁcation 110 Validation 111 Mass Transport in 2-D Models 114 Analysis of Convective and Diffusive Transport Phenomena in a CMR 115 Parametric Study of a CMR 120 Inﬂuence of Characteristic Geometrical Parameters 123 Inﬂuence of the Morphological Membrane Parameters in the Catalyst Layer 124 Inﬂuence of the Operating Conditions 127 Conclusion 130 References 130 Packed-Bed Membrane Reactors 133 Christof Hamel, Ákos Tóta, Frank Klose, Evangelos Tsotsas, and Andreas Seidel-Morgenstern Introduction 133 Principles and Modeling 134 Reactant Dosing in a Packed-Bed Membrane Reactor Cascade 134 Modeling Single-Stage and Multi-Stage Membrane Reactors 136 Simpliﬁed 1-D Model 136 More Detailed 1+1-D Model 137 Detailed 2-D Modeling of a Single-Stage PBMR 139 Model-Based Analysis of a Distributed Dosing via Membranes 140 Model Reactions 140 Simulation Study for ODH of Ethane Using the 1-D Model 141 Experimental 145 Catalyst and Used Membrane Materials 145 Single-Stage Packed-Bed Membrane Reactor in a Pilot-Scale 145

VII

VIII

Contents

5.4.3 5.4.4 5.4.5 5.4.6 5.5 5.5.1 5.5.2 5.5.3 5.5.4 5.5.5 5.6 5.6.1 5.6.2 5.7

6 6.1 6.2 6.2.1 6.2.2 6.2.2.1 6.2.2.2 6.2.3 6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5 6.3.6 6.3.7 6.3.8 6.4

Reference Concept – Conventional Fixed-Bed Reactor 147 Multi-Stage Membrane Reactor Cascade 147 Analytics 147 Experimental Conditions 148 Results for the Oxidative Dehydrogenation of Ethane to Ethylene 148 Comparison Between PBR and PBMR Using Ceramic Membranes in a Single-Stage Operation Mode 148 2-D Simulation Results – Comparison Between PBR and PBMR 152 Application of Sintered Metal Membranes for the ODH of Ethane 153 Investigation of a Membrane Reactor Cascade – Impact of Dosing Proﬁles 155 Quantitative Comparison of the Investigated Reactor Conﬁgurations 157 Results for the Oxidative Dehydrogenation of Propane 158 Comparison Between PBR and a Single-Stage PBMR Using Ceramic Membranes 158 Investigation of a Three-Stage Membrane Reactor Cascade 159 Summary and Conclusions 160 Special Notation not Mentioned in Chapter 2 161 Latin Notation 161 Greek Notation 162 References 162 Fluidized-Bed Membrane Reactors 167 Desislava Tóta, Ákos Tóta, Stefan Heinrich, and Lothar Mörl Introduction 167 Modeling of the Distributed Reactant Dosage in Fluidized Beds 170 Theory 170 Parametric Sensitivity of the Model 173 Bubble Size 173 Secondary Gas Distribution 175 Comparison Between Co-Feed and Distributed Oxygen Dosage 176 Experimental 178 Experimental Set-Up 178 Experimental Procedure 180 Results and Discussions 181 Inﬂuence of the Oxygen Concentration 181 Inﬂuence of the Temperature 183 Inﬂuence of the Superﬁcial Gas Velocity 184 Inﬂuence of the Secondary to Primary Gas Flow Ratio 185 Inﬂuence of Distributed Reactant Dosing with Oxygen in the Primary Gas Flow 187 Conclusions 188 Special Notation not Mentioned in Chapter 2 189

Contents

Latin Notation 189 Greek Notation 190 Subscripts and Superscripts References 190 7

7.1 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 7.2.6 7.3 7.3.1 7.3.2 7.3.3 7.3.4 7.3.5 7.4 7.4.1 7.4.1.1 7.4.1.2 7.4.1.3 7.4.2 7.4.2.1 7.4.2.2 7.4.2.3 7.4.3 7.4.3.1 7.4.3.2 7.5

190

Solid Electrolyte Membrane Reactors 193 Liisa Rihko-Struckmann, Barbara Munder, Ljubomir Chalakov, and Kai Sundmacher Introduction 193 Operational and Material Aspects in Solid Electrolyte Membrane Reactors 194 Classiﬁcation of Membranes 194 Ion Conductivity of Selected Materials 195 Membrane–Electrode–Interface Design in Solid Electrolyte Membrane Reactor 196 Operating Modi of Solid Electrolyte Membrane Reactors 198 Cell Voltage Analysis 199 Non-Faradaic Effects 200 Modeling of Solid Electrolyte Membrane Reactors 201 Reactor Model for Systems Containing Solid Electrolyte Membranes 202 Kinetic Equations for Charge Transfer Reactions 206 Parameters for Charge Transfer and Solid Electrolyte Conductivity 206 Analysis of Maleic Anhydride Synthesis in Solid Electrolyte Membrane Reactor 209 Analysis of Oxidative Dehydrogenation of Ethane in a Solid Electrolyte Packed-Bed Membrane Reactor 212 Membrane Reactors Applying Ion-Conducting Materials 216 High-Temperature Oxygen Ion Conductors 216 Solid Oxide Fuel Cell for Electrical Energy Production 216 Oxidative Coupling of Methane to C2 and Syngas from Methane 217 Dry Reforming of Methane 218 High-Temperature Proton Conductors 219 Hydrogen Sensors and Pumps 220 Fuel Cells 221 Electrocatalytic Membrane Reactors 221 Low-Temperature Proton Conductors 222 PEM Fuel Cells 223 Proton Exchange Membrane Reactors 224 Conclusions 228 Special Notation not Mentioned in Chapter 2 228 Latin Notation 228 Greek Notation 229 Characteristic Dimensionless Numbers 229

IX

X

Contents

Superscripts 230 References 230 8 8.1 8.2 8.2.1 8.2.2 8.2.2.1 8.2.2.2 8.2.3 8.2.3.1 8.2.3.2 8.3 8.3.1 8.3.1.1 8.3.1.2 8.3.2 8.3.2.1 8.3.2.2 8.3.2.3 8.4

9 9.1 9.2 9.2.1 9.2.2 9.2.3 9.3

Nonlinear Dynamics of Membrane Reactors 235 Michael Mangold, Fan Zhang, Malte Kaspereit, and Achim Kienle Introduction 235 Limit of Chemical Equilibrium 235 Reference Model 235 Isothermal Operation 237 Nonreactive Membrane Separation 237 Membrane Reactor 240 Nonisothermal Operation 245 Formation of Traveling Waves 245 Formation of Discontinuous Patterns 246 Pattern Formation 248 Analysis of a Simple Membrane Reactor Model 249 Analysis of Steady-State Reactor Behavior for Vanishing Heat Dispersion 252 Inﬂuence of Heat Dispersion 254 Detailed Membrane Reactor Model 255 Main Model Assumptions 256 Model Equations of the Membrane 257 Simulation Results 259 Conclusions 259 References 261 Comparison of Different Membrane Reactors 263 Frank Klose, Christof Hamel, and Andreas Seidel-Morgenstern General Aspects Regarding Membrane Reactors of the Distributor Type 263 Oxidative Dehydrogenation of Ethane in Different Types of Membrane Reactors 264 Packed-Bed Membrane Reactor 265 Fluidized-Bed Membrane Reactor 265 Electrochemical Packed-Bed Membrane Reactor 266 General Conclusions 266 Reference 267 Index

269

XI

Preface The chemical and pharmaceutical industries are characterized by the fact that a very large spectrum of different target compounds is synthesized. Due to the variety of the physical and chemical properties of the reactants and products involved a wide spectrum of operating conditions and reactor concepts is applied (Moulijn et al., 2001). Despite the long history of chemical reaction engineering there are still many problems which are not solved in a satisfactory manner (Levenspiel, 1999). One of the most difﬁcult problems motivated the research leading to this book. This problem lies in the fact that during the synthesis of a certain target component typically undesired parallel or consecutive reactions occur which reduce the achievable yields. Formed side products have to be separated from the target product at the reactor outlets, which is a demanding and expensive task. Thus, there is considerable interest in developing technologies which allow increasing the selectivity and yield with which a certain target product can be generated. It is well known that the selectivity in reaction networks towards a target compound can be increased following various concepts. First, a careful selection of the reaction temperature can be made to favor the formation of the target. A second, more versatile and very important direction is connected with the intensive activities devoted to developing and applying dedicated catalysts which accelerate speciﬁcally the desired reaction (Ertl et al., 2008). The third approach, which is studied in this book, exploits the fact that the selectivity with respect to a certain desired product can be increased by properly adjusting the local concentrations of the reactants involved. Innovative distributing and dosing concepts have for some time been an objective of research in chemical reaction engineering (Levenspiel, 1999). Besides adding certain reactants in a discrete manner into chemical reactors, various possibilities have been suggested for using different porous or non-porous membranes in order to arrange different ways of contacting the reactants (Coronas, Menendez, and Santamaria,1994; Lu et al., 1997; Seidel-Morgenstern, 2005). Although the membrane reactor concept has been identiﬁed as interesting and promising, there are still several difﬁcult problems that must be solved prior to an industrial application. Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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Preface

This book describes results obtained within the research project “Membrane supported reaction engineering”, which was funded by the German Research Foundation (DFG) and was carried out between 2001 and 2008 at the Otto von Guericke University and the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg (Germany). Chemists, chemical engineers and mathematicians worked in this project together in order to investigate various options of the so-called distributor type of membrane reactors (Dittmeier and Caro, 2008). The projects focused on a single and important class of reactions, namely the selective oxidations of gaseous alkenes. These reactions require typically elevated temperatures and suffer from severe selectivity limitations (Hodnett, 2000). Different types of membranes and reactor conﬁgurations were studied, concentrating on the oxidative dehydrogenation of ethane to ethylene. In order to allow a comparison of the results of different project partners working on packed-bed membrane reactors, ﬂuidized membrane reactors and electrochemical membrane reactors, the same type of vanadia-based catalyst was always used. To implement a range of dosing concepts various high-temperature-resistant membranes were applied. On the one hand, this book was written to summarize the large amount of experimental material generated during the project. On the other hand, it was also the goal of the authors to provide theoretical concepts which allow quantitative descriptions and evaluations of the various types of membrane reactors investigated. The book starts in Chapter 1 with an introduction into some basics of chemical reaction engineering. The equations presented are helpful to evaluate in a quantitative manner the potential of dosing reactants via reactor walls, as applied in membrane reactors of the distributor type, in order to enhance the selectivity of producing a certain target component in a network of reactions. Chapter 2 gives a summary of the current state of the art of modeling packedbed reactors. This chapter serves to introduce the overall notation and provides a frame for modeling mass and heat transfer processes relevant in the different reactors studied. Appropriate model reduction methods, discretization techniques and suitable solvers for the typically large systems of algebraic equations are also discussed in this chapter. Chapter 3 introduces the heterogeneously catalyzed oxidative dehydrogenation (ODH) of ethane which was studied as a model reaction in various projects. Although this reaction is currently far from a wide industrial application, it was identiﬁed to be a suitable object of investigation for the purpose of the overall project. Chapter 3 provides further an important basis for the experimentally oriented projects described later. It summarizes the preparation, characterization and properties of the vanadia catalysts used, the reaction network and a model capable of quantifying the reaction kinetics. The aim of Chapter 4 is the analysis of the relevant transport phenomena, in particular the superposition of convection and diffusion processes. Another point addressed in this chapter is the experimental and theoretical analysis of transport processes in membranes. Finally, an analysis of the inﬂuence of membrane geometry and structural parameters as well as of the operating conditions is performed for reactors with catalytically coated membranes. Hereby, some aspects of the

Preface

numerical solution of the corresponding differential equations are discussed from a mathematical point of view. Chapter 5 describes results of a theoretical study of a packed-bed membrane reactor using models of different levels of complexity. Hereby, membrane reactor tubes are ﬁlled with particles of the solid catalyst. The chapter further summarizes the results of detailed experimental investigations of single- and multi-stage packed-bed membrane reactors as well as conventional packed-bed reactors carried out in laboratory- and pilot-scale reactor set-ups. Besides the ODH of ethane also the ODH of propane was considered. Chapter 6 summarizes the results of an extensive experimental and theoretical investigation devoted to evaluating the potential of porous membranes which are dipped into a bed of ﬂuidized catalyst particles and which serve as an oxygen distributor. This chapter also discusses beneﬁts and limitations of this reactor concept compared to the classic co-feed reactant dosing applied in a conventional ﬂuidized bed reactor. Chapter 7 introduces electrochemical membrane reactors equipped with ionconducting membranes, which are ideally impermeable for non-charged species. These reactors operate as electrochemical cells in which the oxidation and reduction reactions are carried out separately on catalyst/electrode layers located on opposite sides of the electrolyte. The working principle of a solid electrolyte membrane reactor is introduced. Further, material aspects and the modeling of solid electrolyte membrane reactors are discussed. The synthesis of maleic anhydride and again the oxidative dehydrogenation of ethane are considered as experimental examples. Chapter 8 provides insight on nonlinear phenomena that may occur in membrane reactors. It is demonstrated that such reactors can become instable, when membranes are used for side-injection of reactants in order to enhance yields. Under certain conditions, spatially homogeneous solutions can give rise to concentration and temperature patterns which may be quite complex. In the ﬁnal Chapter 9 the results achieved for the different reactor conﬁgurations are compared and a short summary is given to evaluate the current state of membrane reactors of the distributor type. This book is seen by the authors as a contribution to the actively investigated wider ﬁeld of integrated chemical processes (Sundmacher et al.) and more speciﬁcally to membrane reactors combining reaction and separation steps (Sanchez Marcano and Tsotsis, 2002). The editor is very grateful to all colleagues in Magdeburg who contributed to this book for their inspiring, fruitful and pleasant cooperation during the period of this project. All authors thank the German Research Foundation for generous ﬁnancial support, in particular Dr. Bernd Giernoth for his help in all organizational issues, and Hermsdorfer Institut für Technische Keramik for providing membrane samples. We also would like to express our gratitude to Wiley-VCH, in particular Drs. Rainer Münz and Martin Graf, for their professional support and patience during the preparation of this manuscript.

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Finally, the editor wants to express his personal thanks to Marion Hesse, Nancy Cassel and Dr. Christof Hamel for their immense support during the course of administrating the research project and editing this book. Magdeburg, August 2009

Andreas Seidel-Morgenstern

References Coronas, J., Menendez, M., and Santamaria, J. (1994) Methane oxidative coupling using porous ceramic membrane reactors. Chem. Eng. Sci., 49, 2015–2025. Dittmeier, R., and Caro, J. (2008) Catalytic membrane reactors, in Handbook of Heterogeneous Catalysis (eds G. Ertl, H. Knözinger, F. Schüth, and J. Weitkamp), Wiley-VCH Verlag GmbH, Weinheim, pp. 2198–2248. Ertl, G., Knözinger, H., Schüth, F., and Weitkamp, J. (eds) (2008) Handbook of Heterogeneous Catalysis, vol. 8, Wiley-VCH Verlag GmbH, Weinheim. Hodnett, B.K. (2000) Heterogeneous Catalytic Oxidation: Fundamental and Technological Aspects of the Selective and Total Oxidation of Organic Compounds, John Wiley & Sons, Ltd. Levenspiel, O. (1999) Chemical Reaction Engineering, 3rd edn, John Wiley & Sons, Inc., New York.

Lu, Y.L., Dixon, A.G., Moder, W.R., and Ma, Y.H. (1997) Analysis and optimization of cross-ﬂow reactors with distributed reactant feed and product removal. Catal. Today, 35, 443–450. Moulijn, J.A., Makkee, M., and van Diepen, A.E. (2001) Chemical Process Technology, John Wiley & Sons, Ltd, Chichester. Sanchez Marcano, J.G., and Tsotsis, T.T. (2002) Catalytic Membranes and Membrane Reactors, Wiley-VCH Verlag GmbH, Weinheim. Seidel-Morgenstern, A. (2005) Analysis and experimental investigation of catalytic membrane reactors, in Integrated Chemical Processes (eds K. Sundmacher, A. Kienle, and A. Seidel-Morgenstern), Wiley-VCH Verlag GmbH, Weinheim, pp. 359–389. Sundmacher, K., Kienle, A., and SeidelMorgenstern, A. (eds) (2005) Integrated Chemical Processes, Wiley-VCH Verlag GmbH, Weinheim.

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List of Contributors Lyubomir Chalakov Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany now Güntner AG & Co. KG Hans-Güntner-Str. 2–6 82256 Fürstenfeldbruck Germany Velislava Edreva Otto-von-Guericke-Universität Magdeburg Institut für Verfahrenstechnik Lehrstuhl für Thermische Verfahrenstechnik Universitätsplatz 2 39106 Magdeburg Germany Katya Georgieva-Angelova Otto-von-Guericke-Universität Magdeburg Institut für Strömungstechnik und Thermodynamik Universitätsplatz 2 39106 Magdeburg Germany now

ANSYS Germany Staudenfeldweg 12 83624 Otterﬁng Germany Henning Haida Otto-von-Guericke-Universität Magdeburg Institut für Verfahrenstechnik Lehrstuhl für Chemische Verfahrenstechnik Universitätsplatz 2 39106 Magdeburg Germany Christof Hamel Otto-von-Guericke-Universität Magdeburg Institut für Verfahrenstechnik Lehrstuhl für Chemische Verfahrenstechnik Universitätsplatz 2 39106 Magdeburg Germany Stefan Heinrich Technische Universität Hamburg-Harburg Institut für Feststoffverfahrenstechnik und Partikeltechnologie Denickestr. 15 21073 Hamburg Germany

Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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List of Contributors

Arshad Hussain Otto-von-Guericke-Universität Magdeburg Institut für Verfahrenstechnik Lehrstuhl für Thermische Verfahrenstechnik Universitätsplatz 2 39106 Magdeburg Germany now NTNU Department of Chemical Engineering 7491 Trondheim Norway Milind Joshi Otto-von-Guericke-Universität Magdeburg Institut für Verfahrenstechnik Lehrstuhl für Chemische Verfahrenstechnik Universitätsplatz 2 39106 Magdeburg Germany now Reaction Engineering BASF SE GCE/R – M311 67056 Ludwigshafen Germany Malte Kaspereit Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany

Achim Kienle Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany and Otto-von-Guericke-Universität Magdeburg Institut für Automatisierungstechnik Universitätsplatz 2 39106 Magdeburg Germany Frank Klose Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany now Südchemie AG Waldheimerstr. 13 83052 Bruckmühl/ Heufeld Michael Mangold Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany Lothar Mörl Otto-von-Guericke-Universität Magdeburg Institut für Apparate und Umwelttechnik Universitätsplatz 2 39106 Magdeburg Germany

List of Contributors

Barbara Munder Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany

Yuri Suchorski Institute of Materials Chemistry Vienna University of Technology Veterinärplatz 1 1210 Vienna Austria

Liisa Rihko-Struckmann Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany

Kai Sundmacher Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany

Jürgen Schmidt Otto-von-Guericke-Universität Magdeburg Institut für Strömungstechnik und Thermodynamik Universitätsplatz 2 39106 Magdeburg Germany and Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany Andreas Seidel-Morgenstern Otto-von-Guericke-Universität Magdeburg Institut für Verfahrenstechnik Lehrstuhl für Chemische Verfahrenstechnik Universitätsplatz 2 39106 Magdeburg Germany Piotr Skrzypacz Institut für Analysis und Numerik Universitätsplatz 2 39106 Magdeburg Germany

and Otto-von-Guericke-Universität Magdeburg Institut für Verfahrenstechnik Lehrstuhl für Systemverfahrenstechnik Universitätsplatz 2 39106 Magdeburg Germany Sascha Thomas Fraunhofer-Institut für Fabrikbetrieb und -automatisierung Sandtorstrasse 22 39106 Magdeburg Germany Lutz Tobiska Institut für Analysis und Numerik Universitätsplatz 2 39106 Magdeburg Germany

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List of Contributors

Ákos Tóta Otto-von-Guericke-Universität Magdeburg Institut für Verfahrenstechnik Lehrstuhl für Chemische Verfahrenstechnik Universitätsplatz 2 39106 Magdeburg Germany

Evangelos Tsotsas Otto-von-Guericke-Universität Magdeburg Institut für Verfahrenstechnik Lehrstuhl für Thermische Verfahrenstechnik Universitätsplatz 2 39106 Magdeburg Germany

now

Helmut Weiß Otto-von-Guericke-Universität Magdeburg Institut für Chemie Universitätsplatz 2 39106 Magdeburg Germany

Linde AG Linde Engineering Division Dr.-Carl-von-Linde-Str. 6–14 85049 Pullach Germany Desislava Tóta Otto-von-Guericke-Universität Magdeburg Institut für Apparate und Umwelttechnik Universitätsplatz 2 39106 Magdeburg Germany now Linde AG Linde Engineering Division Dr.-Carl-von-Linde-Str. 6–14 85049 Pullach Germany

Tanya Wolff Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany Fan Zhang Max-Planck-Institut für Dynamik komplexer technischer Systeme Sandtorstr. 1 39106 Magdeburg Germany

1

1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors Sascha Thomas, Christof Hamel, and Andreas Seidel-Morgenstern

1.1 Challenges in Chemical Reaction Engineering

Currently there are more then 30 000 specialty chemicals produced industrially from approximately 300 intermediate chemicals (Moulijn, Makkee, and Diepen, 2001). The vast majority of these intermediates are produced from a very limited number of approximately 20 simple base chemicals for example, ethylene, propylene, butane, ammonia, methanol, sulfuric acid and chlorine. To perform efﬁciently the large spectrum of chemical reactions of interest an arsenal of speciﬁc reactor types and dedicated operating regimes has been developed and is applied in various industries. The design of efﬁcient and reliable reaction processes is the core subject of Chemical Reaction Engineering, a discipline which can be considered nowadays as rather mature. The progress achieved and important concepts developed are summarized in several excellent monographs (e.g., Froment and Bischoff, 1979; Schmidt, 1997; Levenspiel, 1999; Missen, Mims, and Saville, 1999; Fogler, 1999). The main starting point of an analysis of reacting systems is typically an evaluation and quantiﬁcation of the rates of the reactions of interest. Hereby, based on the speciﬁc physical an chemical properties of the reactants and products a wider range of temperature and pressure conditions has to be considered during the early development phases. The spectrum of reactor types available and operating principles applicable is very broad. Reactions and reactors are often classiﬁed according to the phases present (Levenspiel, 1999). There are reactions that can be carried out in a single phase. However, in a reaction system often more phases are present requiring more sophisticated conﬁgurations and operation modes. Another useful classiﬁcation is based on the character of the process and distinguishes between continuous and discontinuous (batch) operations. Between these exist semi-batch processes which are often applied to carry out highly exothermal reactions exploiting adjusted dosing concepts (Levenspiel, 1999; Fogler, 1999). To accelerate the desired reactions and/or to inﬂuence the selectivity in reaction networks with respect to the target products, frequently speciﬁc catalysts are Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors

applied. These catalysts might be present in the same phase as the reactants (homogeneous catalysis). To ﬁx these often expensive materials in continuously operated reactors, catalysts are often deposited (immobilized) on the surface of solid porous supports (heterogeneous catalysis). Despite the large efforts devoted to further develop the ﬁeld of Chemical Reaction Engineering, the performance of how chemical reactions are carried out indutrially still suffers from several severe limitations. Very important and not sufﬁciently solved problems are: Problem 1: The rates of chemical reactions leading to desired products are often too low to establish economically attractive processes. Problem 2: The conversion of many reactions of interest is thermodynamically limited, that is, the reactions proceed also in the opposite direction and convert products back (reversible reactions). Problem 3: The energy efﬁciency of endothermal and exothermal reactions performed industrially is often not satisfactory. Problem 4: In reaction networks the selectivities and yields with respect to a certain target product are limited. In recent decades several promising new approaches and innovative reactor concepts have been developed to tackle the mentioned problems. Enhancing the rates of desired reactions (Problem 1) is the main ﬁeld of catalysis. Signiﬁcant progress has been achieved in recent years, both in homogeneous catalysis (e.g., Bhaduri and Mukesh, 2000) and heterogeneous catalysis (e.g., Ertl et al., 2008). To overcome equilibrium limitations (Problem 2) new reactor concepts have been suggested and developed. One of the most successful concepts in this area is reactive distillation which is based on separating certain reactants from each other directly in the reactor (column) by distillation. Thus, undesired backward reactions can be suppressed (Sundmacher and Kienle, 2003). The subject of integrating also other separation processes into chemical reactors is discussed, for example, in a review (Krishna, 2002) and a more recently published book (Sundmacher, Kienle, and Seidel-Morgenstern, 2005). There has long been interest in applying reactor principles which allow for an efﬁcient use of energy (Problem 3) when developing new reaction processes. Recently developed elegant autothermal reactor concepts exploit dedicated heat transfer processes and the dynamics of periodically operated reactors (Eigenberger, Kolios, and Nieken, 2007; Silveston, 1998). Examples of new reactor types include the reversed ﬂow reactor (Matros and Busimovic, 1996) and the loop reactor (Sheintuch and Nekhamkina, 2005). One of the most difﬁcult problems in chemical reaction engineering is to navigate in a reaction network efﬁciently in order to optimize the production of the desired target component (Problem 4). In this ﬁeld again catalysis is a main tool. In recent years many new and highly selective catalysts have been developed, allowing an increase in the selectivity and yield with which many base chemicals,

1.2 Concepts of Membrane Reactors

intermediates and ﬁne chemicals can be produced (Ertl et al., 2008). Complementarily there are permanent activities devoted to identifying the most suitable reactor types and applying the most beneﬁcial operating conditions in order to achieve high selectivities and yields. In this important ﬁeld new reactor types can be expected for the future. One promising option considered when tackling Problem 4 and the subject of this book is to apply optimized dosing strategies using speciﬁc membrane reactors. Before introducing the basic principle of these reactors, the broader ﬁeld of membrane reactors is brieﬂy introduced in the next section.

1.2 Concepts of Membrane Reactors

The application of membranes which divide two speciﬁc parts of a reactor possesses the potential to improve in various ways the performance of chemical reactors compared to conventional reactor concepts. For this reason membrane reactors have long been the focus of intensive research. The state of the art regarding this rather broad ﬁeld has been described in several reviews (Zaspalis and Burggraaf, 1991; Saracco et al., 1999; Dittmeyer, Höllein, and Daub, 2001; Dixon, 2003; Seidel-Morgenstern, 2005). Comprehensive summaries were recently given by (Sanchez Marcano and Tsotsis, 2002; Dittmeyer and Caro, 2008). Modern developments were reported on a regular basis during the “International Congresses on Catalysis in Membrane Reactors” (ICCMR, 1994–2009). Due to the availability of the mentioned extensive overviews and conference proceedings it is not the goal of this chapter to review the ﬁeld again. To introduce the main principles suggested and partly already applied, just a short overview is given below. Figure 1.1 illustrates schematically six membrane reactor concepts (I–VI) related to different problems which should be tackled using membranes within the reactor. For illustration, and because it is frequently the competing principle, at the top of the ﬁgure the classic tubular reactor is shown. This reactor possesses closed walls. Thus, the reactants are typically introduced together at the reactor inlet (co-feed mode). Often tubular reactors are ﬁlled with solid catalyst particles in order to increase the rates and selectivities. This classic ﬁxed-bed or packed-bed reactor (PBR) is intensively studied and used widely (Eigenberger, 1997). It serves as a reference in several sections of this book. Concept I: Retainment of homogeneous catalysts The ﬁrst membrane reactor concept shown in Figure 1.1 exploits the membrane to retain in the reactor soluble (homogeneous) catalysts. Thus, it allows for continuous operation without the need to separate and recycle the typically valuable catalysts. An introduction into the concept is given, for example, by (Cheyran and Mehaaia, 1986; Sanchez Marcano and Tsotsis, 2002). Successful application for various synthesis reactions are described, for example, by (Kragl and Dreisbach, 2002).

3

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1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors

Conventional packed-bed reactor (PBR) Reactants

Products

Catalyst

Different concepts of membrane reactors I

II Homogeneous Catalyst

Reactants

JA

A A+B

Membrane J i (i ⴝ Catalyst)

Products

III

A

JB

B

Catalyst A B+C

C

A

JB

B

D

V

Sweep

Catalyst

C

C

IV

Sweep

A

C

A

q·

C

B+C

JB

D+B

E

q·

E

VI A+B D+B

D U

JD

U

A

D

B

Figure 1.1 Illustration of the conventional packed bed reactor (PBR) and six membrane reactor concepts (I–VI). Concept I: catalyst retainment. Concept II: membrane as “contactor”. Concept III: membrane as

A+B D+B

D U

D

JB

“extractor” (shift of equilibria). Concept IV: coupling of reactions. Concept V: membrane as “extractor” (removal of intermediates). Concept VI: “distributor” (reactant dosing).

Concept II: Contactor Another interesting and promising membrane reactor principle is based on applying the membrane as an active “Contactor”. The reactants are fed into the reactor from different sides and react within the membrane (Miachon et al., 2003; Dittmeyer and Caro, 2008). There are signiﬁcant efforts in order to exploit this principle for heterogeneously catalyzed gas/liquid reactions (three-phase membrane reactors) (Dittmeyer and Reif, 2003; Vospernik et al., 2003).

1.2 Concepts of Membrane Reactors

Concept III: Extractor A widely studied and rather well understood type of membrane reactors is the so-called “Extractor” which removes selectively from the reaction zone certain products via a membrane. As already recognized early (Pfefferie, 1966), this concept possesses the potential to enhance the conversion if the reactions are reversible. To remove the permeated products and to increase the driving force for the transport, additional sweep gases or solvents are needed to apply the “Extractor” principle. Several systematic studies were carried out (e.g., Itoh et al., 1988; Ziaka et al., 1993; Kikuchi, 1997; Schramm and Seidel-Morgenstern, 1999; Schäfer et al., 2003). An evaluation of the potential considering also the additional sweep gas is given e.g. by (Seidel-Morgenstern, 2005). Concept IV: Energetic coupling Membranes can be also used to separate two reactor segments in which different reactions take place (Gryaznov, Smirnov, and Mischenko, 1974). The courses of these reactions are inﬂuenced when there is a selective transport of certain components which participate in both reactions (e.g., component B in the Figure 1.1). Reactive sweep gases might further improve the performance of the “Extractor” concept described above. If the two reactions are endothermal and exothermal an attractive thermal coupling can be realized (e.g., Gobina, Hou, and Hughes, 1995). In this case an additional heat ﬂux over the membrane takes place which offers interesting degrees of freedom to optimize the reactor from an energetic point of view (Eigenberger, Kolios, and Nieken, 2007). Concept V: Selectivity enhancement through withdrawal of a product This concept resembles concept III. However, the component of interest that should be removed (“Extraction”) via the membrane is an intermediate component generated in a network of reactions. This removal leads to the reduction or complete avoidance of undesired consecutive reactions and, thus, to enhanced selectivities with respect to this target component (Kölsch et al., 2002; Dittmeyer and Caro, 2008). Unfortunately, the application of this elegant principle requires very selective membranes which are often not available for industrially relevant problems. Concept VI: Selectivity enhancement through optimized reactant dosing (distributor) The main focus of this book is to contribute to achieve higher selectivities and yields and thus tackling Problem 4 mentioned above. Hereby, an interesting and attractive approach is based on using membranes to dose (distribute) certain reactants into the reactor. Compared to conventional PBR operation different local concentrations and residence time characteristics can be established and exploited to enhance selectivities. Although the general idea has long been known and signiﬁcant efforts have been undertaken to exploit the potential of the concept (e.g., Mallada, Menendez, and Santamaria, 2000; Al-Juaied, Lafarga, and Varma, 2001; references in Section 1.8), no industrial applications of such a “Distributor” type of membrane reactor have been reported. In implementing the concept, several degrees of freedom can be exploited. Some important questions considered in more or less detail in this book are:

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1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors

•

Which component should be dosed via the membrane and which should be introduced at the reactor inlet?

•

Which kind of membrane and which separation mechanism should be exploited?

•

To what extent does multi-stage dosing improve the performance compared to the application of a simple uniform dosing proﬁle?

•

Is a particulate catalyst (as used in the packed-bed membrane reactor, PBMR) more suitable than a thin catalytic layer on the membrane surface (as used in a catalytic membrane reactor, CMR)?

•

What is the dynamic behavior of such a conﬁguration?

Before discussing in more detail some reaction engineering aspects related to the selectivity problem, a short overview is given concerning the ﬁeld of membrane materials and types.

1.3 Available Membranes

During the past decades a broad spectrum of different membrane types was developed. Extensive overviews are available (e.g., Bhave, 1991; Ohlrogge and Ebert, 2006; Peinemann and Pereira Nunes, 2007). The two most suitable classiﬁcation categories are related to: (a) the membrane materials and (b) the membrane permeabilities and selectivities. Concerning the materials a distinction can be made between organic and inorganic membranes. Organic polymeric membranes can be synthesized with very speciﬁc properties using well developed concepts of macromolecular chemistry. Hereby, a large ﬂexibility exists and a broad spectrum of materials can be made with properties adjusted to the speciﬁc separation problem. A drawback of organic membranes is their limited thermal stability. At higher temperatures only inorganic membranes can be applied. Also in this area there is a broad spectrum of membranes available based, for example, on ceramics, perovskites, metals, metal alloys and composites of these materials (e.g., Julbe, Farrusseng, and Guizard, 2001; Verweij, 2003). Another classiﬁcation distinguishes between dense and porous membranes. Whereas dense membranes offer typically high selectivities for certain components, they suffer from limited permeabilities. Overviews are given, for example, by (Dittmeyer, Höllein, and Daub, 2001) for metal membranes and by (Bouwmeester, 2003) for ion- and electron-conducting materials. The transport behavior is opposite when porous membranes are applied, allowing for higher ﬂuxes but providing limited selectivities. Porous membranes are typically classiﬁed according to their pore size, deﬁning the various types af membrane separation processes as, for example, microﬁltration, ultraﬁltration and nanoﬁltration (Li, 2008).

1.3 Available Membranes

Besides pore size the chemistry of the membrane surface also plays an important role. Traditionally membranes are used to carry out transport and separation processes. In such applications they are chemically inert. Membranes might also possess certain surface properties which catalyze chemical reactions. Such catalytically active membranes are of particular interest for the “Contactor” type of membrane reactors. However, they might be applicable also in some of the other membrane reactor concepts depicted in Figure 1.1. The quantitative description and prediction of component speciﬁc transport rates through dense and porous membranes has been studied intensively. Introductions into the transport theories available are given, for example, by (Mason and Malinauskas, 1983; Sahimi, 1995; Wesselingh and Krishna, 2000; Bird, Stewart, and Lightfoot, 2002). Speciﬁc problems of quantifying accurately transport rates are often related to the composite structure of the membranes of interest (Thomas et al., 2001). The accurate prediction of permeabilities and separation factors is still a difﬁcult task and the subject of further intensive research. In general, the identiﬁcation, provision and quantitative description of materials suitable to tackle a speciﬁc separation problem is still not a routine task. There is a particular aspect related to membrane reactors which is addressed in Section 1.7. A successful operation requires a sufﬁcient kinetic compatibility of the rates of the transport through the membranes and the rates of the reactions of interest. Evaluating the general potential of membrane technology Burggraaf and Cot predicted already in 1996 that membrane reactors possess a signiﬁcant and growing potential in particular for high-temperature reactions using inorganic membranes (Figure 1.2; Burggraaf and Cot, 1996).

Market penetration

e: nc a br tion em ara m p er se ym uid l po liq : e: : ce nc a ce an n r br tion a b br em a em n m ar em ion m atio ic sep m t ic r m er ara am pa ra id re- rs ce liqu ym sep cer s se l atu acto r o e p as ga emp es re g h t an hig mbr me

1980

1990

2000

Figure 1.2 Quantitative scheme of expected market penetration as a function of time for different groups of membrane applications (reprinted from [Burggraaf and Cot, 1996], with permission).

7

8

1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors

1.4 Illustration of the Selectivity Problem

Impressive and frustrating examples characterizing the dilemma and importance of the selectivity problem introduced in Section 1.1 as Problem 4 were given for the industrially important class of partial oxidation reactions by (Haber, 1997; Hodnett, 2000). The latter author presented a large number of selectivity versus conversion plots for various hydrocarbon oxidations. An example is shown in Figure 1.3 for the partial oxidation of n-butane to maleic anhydride catalyzed by a vanadium phosphorus oxide (VPO) catalyst. In this plot the results of various studies reported in the literature are superimposed. Hereby, different reactor types and catalysts were applied. There is obviously a clear border which current technology cannot pass. For other reactions of this type which are applied in a large scale the “dream corner” (100% selectivity, 100% conversion) is even more remote. The problem described for oxidation reactions exists in a similar manner for the important class of selective hydrogenation reactions. As mentioned above, selectivity improvements are the objective of intensive research in catalysis. Examples of successful new catalysts were summarized by (Ertl et al., 2008). However, there are still many “dream reactions” for which satisfactory catalysts are not yet available. The alternative way to improve selectivities is to develop better reactors using currently available catalysts. In this case it is particularly important to understand the relation between local concentrations and temperatures and the selectivity–conversion behavior. To follow this second route is the focus of this book. The next section summarizes a few basics of chemical reaction engineering which are important for understanding how membrane reactors of the distributor type can contribute to achieve improvements in selectivities and yields.

Figure 1.3 Multiple selectivity–conversion plot for n-butane selective oxidation to maleic anhydride over a range of catalysts and in a variety of reaction conditions (reprinted from Hodnett, 2000, with permission).

1.5 Reaction Rate, Conversion, Selectivity and Yield

1.5 Reaction Rate, Conversion, Selectivity and Yield

In order to evaluate the potential of membrane reactors in general and “Distributors” in particular, the classic approaches of chemical reaction engineering are available. Basic aspects of analyzing and optimizing various types of chemical reactors have been discussed extensively in standard textbooks of the ﬁeld (e.g., Levenspiel, 1999; Fogler, 1999). Below is given a selected summary introducing important quantities and performance criteria. 1.5.1 Reaction Rates

The reaction rates are the key information required to quantify chemical reactions and to describe the performance of chemical reactors. The rate of a single reaction in which N components are involved is deﬁned as: rScale =

1 1 dni Scale ν i dt

i = 1, N

(1.1)

Reaction

The use of the stoichiometric coefﬁcient νi guarantees that the reaction rate does not depend on the component i considered. There are several possibilities regarding the selection of an appropriate scale. For reactions taking place in a homogeneous phase, frequently the reaction volume VR is used leading to a reaction rate which has the dimension [mol/m3 s]. In heterogeneous catalysis often the mass or surface area of the catalyst, MCat or ACat, are more useful scaling quantities leading to reaction rates in [mol/kg s] or [mol/m2 s]. Obviously, it is necessary to use rScale and the chosen scaling quantity consistently. If different scales are of relevance, for example, “a” and “b”, it must hold: Scalea rScalea = ScalebrScaleb

(1.2)

To illustrate the relevance of the reaction rate, in this chapter the reactor volume is selected for scaling. For the sake of brevity no scale index is used. Please note that other chapters of this book also use mass-related reaction rates. If the reactor volume VR is assumed to be constant, the reaction rate r can be expressed as: r=

1 dci ν i dt

i = 1, N

(1.3)

where c˜i is the molar concentration of component i deﬁned as: ci =

ni VR

i = 1, N

or for open systems with the (also constant) volumetric ﬂow rate V˙ as:

(1.4)

9

10

1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors

ci =

n i V

i = 1, N

(1.5)

Reaction rates depend on temperature and the molar concentrations (Levenspiel, 1999), that is: r = r (T , c1 , c2 , … , cN )

(1.6)

If only one reaction occurs, knowledge regarding the concentration change of a single key component is sufﬁcient to describe all other concentration changes. 1.5.2 Conversion

If a reactant A is chosen as the key component, its conversion can be deﬁned as: XA =

n A0 − n A n A0

(1.7)

or for constant volumes: XA =

cA0 − cA cA0

(1.8)

The mole numbers n A0 or concentrations cA0 stand here for the initial or inlet states. The conversion can be considered as a dimensionless concentration. Using this quantity Equation 1.6 can be reformulated: r = r (T , cA0 , X A )

(1.9)

The temperature dependence of the reaction rate, r(T), can be accurately described using the well known Arrhenius equation (Levenspiel, 1999). Regarding the conversion (i.e., concentration) dependence, r can be split into a constant contribution r 0 (related to the initial or inlet state) and a conversiondependent function f (XA) describing the rate law valid for the speciﬁc reaction considered: r = r 0 (cA0 ) f ( X A )

(1.10)

1.5.3 Mass Balance of a Plug Flow Tubular Reactor

One of the simplest models used to describe the performance of tubular reactors is the well known isothermal one-dimensional plug ﬂow tubular reactor (PFTR) model. The mass balance of this model is for: (a) steady-state conditions, (b) a network of M simultaneously proceeding reactions and (c) a constant volumetric ﬂow rate V˙ (Froment and Bischoff, 1979; Levenspiel, 1999): dci AR M = ∑ νijr j dz V j =1

i = 1, N

(1.11)

1.5 Reaction Rate, Conversion, Selectivity and Yield

The νij in Equation 1.11 are the elements of the stoichiometric matrix, AR stands for the cross-sectional area of the tube and z is the axial coordinate. With the residence time τ in a reactor section of length z:

τ=

AR z V

(1.12)

the mass balance of the PFTR can be expressed also in the following manner: dci M = ∑ ν ijr j dτ j =1

i = 1, N

(1.13)

The systems of ordinary differential equations (1.11) or (1.13) can be integrated numerically with the initial conditions ci0 = ci (z = 0 or τ = 0) and the speciﬁc rate laws. If only one reaction needs to be considered (M = 1) and the conversion of component A is chosen to be the state variable of interest, the mass balance of the PFTR can be also expressed as follows: dX A (−ν A )r 0 f ( X A ) = dτ cA0

(1.14)

Integration from 0 to the residence time corresponding to the reactor length LR, that is, τ(LR) and from 0 to XA(τ ) leads to the following dimensionless mass balance of the PFTR: X A (τ )

∫

Da =

0

dX A f (X A )

(1.15)

In this equation Da is the Damköhler number (Levenspiel, 1999): Da =

( −ν A ) r 0 τ cA0

(1.16)

which represents the ratio of the characteristic times for convection and reaction. The dimensionless mass balance equation (1.15) can be solved analytically for various simple rate laws f (XA) providing instructive XA(Da) proﬁles. If for example the rate of a reaction A → Products can be described by a simple ﬁrst-order kinetic expression: r = kcA

(1.17)

the dimensionless balance provides with r = kc and f(XA) = 1 − XA: 0

0 A

X A = 1 − e −Da

(1.18)

In contrast, for a second-order reaction with the rate expression: r = kcA2 holds:

(1.19)

11

1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors 1

a

0.8

c

b

0.6

XA

12

0.4

0.2

0 0

1

2

3

4

5

6

7

8

9

10

Da Figure 1.4 Dependence of conversion on Damköhler number for: (a) a ﬁrst-order reaction (1.18), (b) a second-order reaction (1.20) and (c) a second-order reaction with two reactants and a non-stoichiometric feed composition (Equations 1.21 and 1.22, here for λ = 0.5).

XA=

Da 1+Da

(1.20)

In the case of a bimolecular reaction of the type vAA + vBB → Products the composition of the feed mixture is an important free parameter. This can be conveniently expressed using a stoichiometric feed ratio λ deﬁned as follows:

λ=

νBcA0 ν AcB0

(1.21)

When component B is introduced in excess, that is, when 0 < λ < 1, the solution of the mass balance provides: XA =

e Da(1− λ ) − 1 e Da(1− λ ) − λ

(1.22)

The three different functions described by Equations 1.18, 1.20 and 1.22 are illustrated in Figure 1.4. The curves shown reveal the following two well known and important facts: (a) higher reaction orders require larger Da numbers (i.e., larger residence times) in order to reach the same conversion and (b) an excess of a reactant increases conversion of the other reactant. 1.5.4 Selectivity and Yield

In general, several reactions proceed simultaneously in a reactor. Thus, the selectivity and yield with respect to a certain desired target component D achievable in networks of parallel and series reactions are essential quantities.

1.6 Distributed Dosing in Packed-Bed and Membrane Reactors

The integral selectivity with respect to the desired component D, SD, is related to the corresponding consumption of the reactant A. Considering the molar ﬂuxes of the components at the inlet and outlet of a continuously operated reactor, SD is deﬁned as follows: SD =

( −ν A )

n D

(n A0 − n A ) vD

(1.23)

Of even more practical relevance is the yield of component D, YD, which is: YD =

n D ( −ν A ) n A0 vD

(1.24)

Obviously, for the yield holds: YD = SD X A

(1.25)

Let us consider a desired “reaction D” leading to the target product D: A+B→D

(1.26)

and an undesired consecutive “reaction U” leading to an undesired product U: D+B→U

(1.27)

The rates of these two reactions could be, for example, described by the following power law kinetics: rD = kD cAα cBβ1

(1.28)

β2 B

(1.29)

δ D

rU = kU c

c

The selectivity and the yield with respect to D depend strongly on the values of the two reaction rate constants kD und kU and on the reaction orders α, β1, β2, δ. Illustrative results assuming that all reaction orders are unity were obtained solving numerically the mass balance equations of the PFTR model (1.13) for three different ratios kD/kU. The courses of the SD(XA) and YD(XA) curves shown in Figure 1.5 reveal the strong impact of the reaction rates. Obviously, it is very desirable to operate in the upper right (“dream”) corners of these plots where all performance criteria (conversion, selectivity and yield) are unity. Obviously, this corner is closer when kD/kU is large.

1.6 Distributed Dosing in Packed-Bed and Membrane Reactors

In networks of parallel-series reactions optimal local reactant concentrations are essential for a high selectivity towards a certain target product. It is well known that it is advantageous to avoid back-mixing when undesired consecutive reactions can occur (e.g., Levenspiel, 1999; Fogler, 1999). This is one of the main reasons why partial hydrogenations or oxidations are performed preferentially in tubular

13

1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors 1.0

a

0.8

0.6

SD

b

0.4

c

0.2

0

0.8

a

0.6

YD

14

b

0.4

0.2

c

0 0

0.2

0.4

0.6

0.8

1.0

XA Figure 1.5 Selectivity SD and yield YD as a function of conversion XA for the two consecutive reactions A + B → D and D + B → U calculated with the PFTR model (1.11), ﬁxing the residence time and varying the feed composition in a wide range. The

reaction rates were described with Equations 1.28 and 1.29 assuming that all reaction orders are unity. Three different ratios of the rate constants of the desired and the undesired reaction were considered: (a) kD/kU = 10, (b) kD/kU = 1, (c) kD/kU = 0.1.

reactors. All reactants enter typically such tubular reactors together at the reactor inlet (co-feed mode, Mode 1 in Figure 1.6). In order to inﬂuence the reaction rates along the reactor length, essentially the temperature remains as the parameter that could be inﬂuenced. However, the realization of a deﬁned temperature modulation in a tubular reactor is not trivial (Edgar and Himmelblau, 1989). An alternative and attractive possibility, also capable to inﬂuence the course of complex reactions in tubular reactors, is to abandon the co-feed mode and to install more complex dosing regimes. It is relatively simple to add one or several of the reactants to tubular reactors in a locally distributed manner. This approach obviously offers a large variety of options differing mainly in the positions at which the components

1.6 Distributed Dosing in Packed-Bed and Membrane Reactors

B L=1

Mode 1

A

L=1

L=1

B A

B

B

Mode 2

A

Mode 3

A

B

L >1

B

L‡ •

Mode 5

A

Mode 6

L‡ •

L‡ •

A

Mode 4

A

B Mode 7

Figure 1.6 Illustration of possible dosing concepts for tubular reactors: conventional reactor (co-feed, Mode 1), possibilities of discrete dosing (Modes 2, 3, 4), possibilities of continuous dosing (Modes 5, 6, 7). L is the number of segments or stages.

are dosed. Figure 1.6 illustrates several possible scenarios differing from the conventional feeding strategy (Mode 1). In the top row are depicted three scenarios of discrete dosing (Modes 2, 3, 4) differing in the positions and amounts of introducing a reactant B along the reactor length. If the number of discrete dosing points L is reduced to one the conventional reactor principle results. In the lower row of Figure 1.6 are illustrated schematically three concepts of dosing continuously over the reactor wall. These concepts are obviously connected with the membrane reactor Concept VI shown in Figure 1.1. Uniform dosing over one reactor segment (Mode 5), stage-wise segmented dosing (Mode 6) and the implementation of a fully continuous dosing proﬁle (Mode 7) are possible options. The larger the number of segments L the more the concepts converge into the continuous dosing proﬁle case (Mode 7). 1.6.1 Adjusting Local Concentrations to Enhance Selectivities

The different dosing concepts illustrated in Figure 1.6 provide different outlet compositions and, thus, performance criteria. To quantify and compare them it is instructive to introduce differential local selectivity with respect to a speciﬁc desired product D, SDdiff , which depends on the local concentrations. Assuming that a valuable reactant A is converted the local selectivity SDdiff can be expressed as a function of the corresponding reaction rates of all M reactions occurring in the reaction network as follows: M

SDdiff =

∑ν

j =1 M

D, j

⋅r j

∑ (−ν A, j )⋅r j j =1

(1.30)

15

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1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors

To evaluate typical trends it is again instructive to consider the simple reaction scheme of two consecutive reactions introduced above (1.26 and 1.27) and the power law rate expressions given by Equations 1.28 and 1.29. In such a case for the differential selectivity with respect to D follows: SDdiff =

rD − rU k (T ) cDδ β2 − β1 = 1− U cB rD kD (T ) cAα

(1.31)

Equation 1.31 clearly reveals that for this reaction scheme and the kinetics assumed an improved differential selectivity SDdiff can be achieved when:

• •

The reactions take please at a temperature which minimizes kU/kD, The concentration D is kept low (favoring a removal of D, for example, with a membrane reactor of the extractor type shown in Figure 1.1 as Concept V),

•

The concentration of A is kept high (i.e., conversion should be restricted and back-mixing avoided; the former fact leading to concepts with a recycle of A, the latter fact favoring tubular reactors compared to stirred tanks),

•

For β2 < β1 a high concentration of B is advantageous, which favors a concentrated feeding of this reactant at the reactor inlet,

•

For β2 > β1 a low concentration of B is advantageous, which can be realized by a distributed feeding of this reactant.

Since these trends are speciﬁc for the reaction scheme and the rate equations considered no generalization is possible. However, a detailed inspection of the speciﬁc differential selectivities allows drawing similar conclusions for other cases. Of special relevance for the example of partial oxidation reactions of hydrocarbons and for the chapters of this book is the following fact. Typically desired oxidation reactions leading to the intermediate products of interest possess lower reaction orders with respect to oxygen compared to the undesired total oxidation reactions leading to carbon dioxide and water (Mezaki and Inoue, 1991). Considering Equation 1.31 and the ﬁnal conclusion listed above leads to the hypothesis that a low oxygen concentration achievable by implementing a spatial distribution can be beneﬁcial for the selectivity with respect to a target component. Such a regime can be realized by the distributor type of membrane reactor shown in Figure 1.1 as Concept VI. 1.6.2 Optimization of Dosing Proﬁles

Knowing the structure of the reaction network of interest and the concrete concentration dependences of the reaction rates allows determining speciﬁc dosing proﬁles which are optimal for a certain reactor conﬁguration. Only for a limited

1.6 Distributed Dosing in Packed-Bed and Membrane Reactors

number of cases characterized by a small number of rate expressions and simple reactor models can analytical results be generated (Hamel et al., 2003; Thomas, Pushpavanam, and Seidel-Morgenstern, 2004). Using a modiﬁed PFTR model the different dosing modes illustrated in Figure 1.6 were analyzed. Mode 1 required just the direct application of Equation 1.11 with the boundary condition describing the co-feed mode of components A and B. Modes 2, 3 and 4 can be simulated using Equation 1.11 in a stagewise manner applying for each segment the boundary conditions corresponding to the speciﬁc discrete dosing approach and the series connection of the segments. To describe dosing over the reactor walls (Modes 5, 6, 7) the mass balance equation of the PFTR has to be extended by an additional transport term as follows: dci AR M P = ∑ νijr j + VR Ji dz V j =1

i = 1, N

(1.32)

In this equation PR is the perimeter of the tube and the Ji are the molar ﬂux densities of the transport of component i through the reactor wall. Hereby, belowspeciﬁc uniform dosing proﬁles (constant Ji) were assumed for each reactor segment. To illustrate the principle and potential of distributed dosing selected results of a case study are summarized. The following three reactions of a parallelconsecutive reaction scheme were considered, converting the two reactants A and B into a desired product D and an undesired product U: A+B→D

(1.33)

A + 2B → U

(1.34)

D+B→U

(1.35)

The rates of these three reactions were described by the following power law kinetics: rD = kD cAαD cBβD

(1.36)

rU1 = kU1 cAαU1 cBβU1

(1.37)

βU2 B

(1.38)

αU2 D

rU2 = kU2 c

c

The reactor model given with Equation 1.32 was solved numerically for selected parameters of these rate expressions. With a sequential quadratic programming (SQP) optimization algorithm (Press et al., 1992) the optimal amounts of component B that should be dosed were determined with the selected objective of maximizing the molar fraction of component D at the reactor outlet. The discrete dosing Mode 3 assuming equidistant feeding positions and the continuous dosing Mode 6 were compared assuming segments of identical length. In a series of optimizations in both cases the numbers of segments L were ﬁxed to the following three values: 1, 3 or 10. Hereby the results of Mode 3 for L = 1 correspond to the

17

18

1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors

conventional co-feed ﬁxed-bed reactor (Mode 1). The speciﬁc degrees of freedom speciﬁed were the L molar ﬂows of component B dosed, n Ddosed, at the inlet of each segment (Mode 3) or over the segment wall (Mode 6, calculated from the optimal JD and the wall area). Below for the purpose of illustration, selected results are presented in Figures 1.7 and 1.8. The calculations were done assuming that the reaction orders are αD = αU1 = αU2 = βD = 1 and βU1 = βU2 = 2. This implies that in the undesired reactions (1.37) and (1.38) the order with respect to D is higher then in the desired reaction (1.36). The rate constants kj were assumed to be identical. A stream of 1 mol/s of pure A was introduced at the inlet of the ﬁrst segment of a reactor possessing an overall volume VR = 0.01 m3. The ﬁgures show over the reduced reactor length the dosed amounts, the total ﬂow rates, the local molar fractions of the dosed component B and those of the other three components, including the optimized molar fraction of D, xD (xi = n˙i/n˙tot). The results obtained for this speciﬁc case provide the following conclusions:

•

For both modes decreasing dosing proﬁles are found to be optimal, that is, the largest amounts are dosed in the segments close to the reactor inlet and lower amounts are dosed into the following segments. Some B is also dosed into the last segment.

•

There is for both modes an increasing amount of D found at the reactor outlet for increasing segment numbers L.

•

The diluted dosing of B leads in comparison to the conventional co-feed mode (discrete dosing, L = 1, Mode 1) to larger molar amounts of D.

•

The continuous dosing (Mode 6, e.g., applied in a membrane reactor) outperforms for the same segment numbers the discrete dosing (Mode 3) as indicated by larger xD at the reactor outlet.

•

For L = 1 there is a signiﬁcant performance increase of Mode 6 compared to the conventional co-feed operation.

•

Already for L = 3 the potential of Mode 6 seems to be reached. Further segmentation does not lead to signiﬁcant further enhancement in xD.

The results of more systematic theoretical studies explaining in more detail the signiﬁcance of the reaction orders regarding the selection of the component that should be dosed and regarding the shapes of suitable dosing proﬁles are available (Lu et al., 1997a, 1997b, 1997c; Hamel et al., 2003; Thomas, Pushpavanam, and Seidel-Morgenstern, 2004). Examples for the application of the above theoretical considerations in concrete case studies are given in the next chapters of this book. As per (Kuerten et al., 2004), limits of the above-used simpliﬁed one-dimensional isothermal membrane reactor model are also discussed.

1.6 Distributed Dosing in Packed-Bed and Membrane Reactors

L=1 (a)

L=3

1.4 1.2

n· dosed B

1

1 0.8

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

0

0

2.5

2.5

2.5

2

2

2

1.5

1.5

1.5

0.6

tot

(c)

xB [-]

1.2

0.8

1 0.8

(b) n·

L=10

1.2

1

1

1

0.5

0.5

0.5

0

0

0

0.6

0.6

0.6

0.5

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0.0

0.0

0.0

1

1

1

0.8

0.8

0.8

(d)

xi [-]

D

D

0.6

U

0.4

0.6

0.6

0.4

0.4

A 0.2

0

U

0.2

A

0

ξ [-]

D

0

1

A

0.2

0

Figure 1.7 Optimized dosed amounts of B, local total molar ﬂuxes and local molar fractions over the reduced reactor length for the discrete dosing Mode 3 and different

ξ [-]

0

1

0

ξ [-]

segment numbers. Kinetic parameters: αD = αU1 = αU2 = βD = 1, βU1 = βU2 = 2, kD = kU2 = kU1 = 104 mol/(s·m3).

U

1

19

20

1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors

L=1 (a)

L=3

1.2

n· dosed B [mol/s]

(b) n· tot [mol/s]

(c)

xB [-]

1.2

1

1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

0

0

2.5

2.5

2.5

2

2

2

1.5

1.5

1.5

1

1

1

0.5

0.5

0.5

0

0

0

0.06

0.06

0.06

0.04

0.04

0.04

0.02

0.02

0.02

0.00

0.00

0.00

1

1

1

(d)

D

D

D

xi [-]

L=10

1.2

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

A

A

A

0.2

0.2

0.2

U

U 0

0

ξ [-]

0

1

0

Figure 1.8 Optimized dosed amounts of B, local total molar ﬂuxes and local molar fractions over the reduced reactor length for the continuous dosing Mode 6 and different

ξ [-]

U 0

1

0

ξ [-]

segment numbers. Kinetic parameters: αD = αU1 = αU2 = βD = 1, βU1 = βU2 = 2, kD = kU2 = kU1 = 104 mol/(s·m3).

1

1.7 Kinetic Compatibility in Membrane Reactors

1.7 Kinetic Compatibility in Membrane Reactors

In order to achieve signiﬁcant effects of membranes introduced into a reactor compared to conventional reactor operation, there should be certain compatibility between the ﬂuxes that pass the membrane and the amounts consumed or produced during the chemical reactions. The speciﬁc amounts related to the simultaneous occurrence of M chemical reactions can be expressed based on Equation 1.1 as follows: dni dt

M

Reaction

= Scale∑ ν ijrScale, j

i = 1, N

(1.39)

j =1

As mentioned before different scales might be appropriate to quantify the reaction rates. Regarding the transport through membranes usually the membrane area AM is the appropriate scaling parameter. The molar ﬂux of a component i through a membrane can be expressed as: n i

Membrane

= AM Ji

i = 1, N

(1.40)

In the above Ji designates, as in Equation 1.32, the molar ﬂux density of component i. Provided there is information available regarding the amounts transformed by the reactions and the amounts that could be transported through the membranes (based on Equations 1.39 and 1.40, respectively), several important questions could be answered in early development stages as, for example,: “how much membrane area must be provided per scale of the reaction zone?” and “is a more detailed investigation of coupling reaction and mass transfer through a speciﬁc membrane justiﬁed?”. Following this approach recently a useful estimation was given by (van de Graaf et al., 1999). Regarding the productivity of reactions, achievable space time yields (STY) of currently operated catalytic reactors were considered. Concerning this quantity currently the following “window of reality” holds: STY =

n Prod mol ≈ 1 − 10 VR m3s

(1.41)

The achievable ﬂuxes through membranes, J, were designated by (van de Graaf et al., 1999) as area time yields (ATY, in mol/m2s). Figure 1.9 provides an estimation of the current state regarding the possibility of matching the two processes. For the wide range of considered membranes, the required ratios of membrane areas to reactor volumes (AM/VR) are between 10 and 100 m−1. These values allow estimating that the diameter of applicable cylindrical tubular reactors should be in a range between 0.04 and 0.4 m. This appears to be a reasonable range for industrial applications indicating that a matching of the two processes under consideration is achievable with currently available membranes.

21

22

1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors

Figure 1.9 Comparison of the space time yield (STY) of catalytic reactors with the area time yield (ATY) of several inorganic membranes (reprinted from [van de Graaf et al., 1999], with permission).

1.8 Current Status of Membrane Reactors of the Distributor Type

There are several profound theoretical and experimental studies at the laboratory scale available which focus on the application of various conﬁgurations of membrane reactors as a reactant distributor in order to improve selectivity–conversion performances. In particular several industrially relevant partial oxidations were investigated. Examples include the oxidative coupling of methane (Coronas, Menedez, and Santamaria, 1994), the oxidative dehydrogenation of propane (Alonso et al., 1999), butane (Tellez, Menedez, and Santamaria, 1997) and methanol (Diakov and Varma, 2003, 2004), the epoxidation of ethylene (Al-Juaied, Lafarga, and Varma, 2001) and the oxidation of butane to maleic anhydride (Mallada, Menedez, and Santamaria, 2000). Speciﬁc aspects of membrane reactors related to carrying out the oxidative dehydrogenation of ethane to ethylene, which are described and studied in detail in this book, were investigated by (Coronas, Menedez, and Santamaria, 1995; Tonkovich et al., 1996). There appears to be potential in using membrane reactors of the distributor type also for other types of reaction networks. Another promising ﬁeld can be for example selective hydrogenations. The hydrogenation of acrolein to allyl alcohol was studied by (Hamel et al., 2005). All the studies mentioned were done exclusively at the laboratory or pilot scale. They focused on high-temperature reactions and applied different types of ceramic membranes. Currently there are no industrial applications applying a membrane reactor of the distributor type on a larger scale. To further promote the promising concept systematic studies are required quantifying both the reaction and transport processes and describing in more detail the processes occurring in such membrane reactors. Hereby, various options applicable with respect to the types of membranes and the reactor principles should be

1.8 Notation used in this Chapter

considered and compared. This book contains various contributions to the mentioned problems. The following chapter summarizes theoretical concepts required to model membrane reactors.

Notation used in this Chapter

ACat AM AR Yi Ji kj L LR M MCat n˙ PR r Si Sidiff T VR V˙ Xi xi z

m2 m2 m2 % mol·s−1·m−2 mol·s−1·m−3 m – kg mol/s m mol·s−1·m−3 % % K m3 mol/s % – m

catalyst surface area membrane surface area cross section area of a tubular reactor yield with respect to component i molar ﬂux density of component i reaction rate constant number of reactor segments length of a tubular reactor or reactor segment number of reactions catalyst mass molar ﬂux perimeter of a tubular reactor rate of reaction integral selectivity with respect to component i differential selectivity with respect to component i temperature reactor volume volumetric ﬂowrate conversion of reactant i molar fraction of component i axial coordinate of tube

Greek Symbols

α β δ λ ν ξ τ

– – – – – – s

reaction order reaction order reaction order stoichiometric feed ratio stoichiometric coefﬁcient non-dimensional axial reactor length, ξ = z/LR residence time

Superscripts and Subscripts

i j

component reaction

23

24

1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors

tot 0

total initial or inlet state

Abbreviations

CMR PBR PBMR

Catalytic membrane reactor Packed bed reactor Packed bed membrane reactor

References Alonso, M.J., Julbe, A., Farrusseng, D., Menendez, M., and Santamaria, J. (1999) Oxidative dehydrogenation of propane on V/Al2O3 catalytic membranes. Effect of the type of membrane and reactant feed conﬁguration. Chem. Eng. Sci., 54, 1265–1272. Al-Juaied, M.A., Lafarga, D., and Varma, A. (2001) Ethylene epoxidation in a catalytic packed-bed membrane reactor: experiments and model. Chem. Eng. Sci., 56, 395–402. Bhaduri, S., and Mukesh, D. (2000) Homogenoeus Catalysis, Wiley-VCH Verlag GmbH, Weinheim. Bhave, R.R. (ed.) (1991) Inorganic Membranes: Synthesis, Characteristics and Applications, Reinhold, New York. Bird, B.B., Stewart, W.E., and Lightfoot, E.N. (2002) Transport Phenomena, John Wiley & Sons, Inc., New York. Bouwmeester, H.J.M. (2003) Dense ceramic membranes for methane conversion. Catal. Today, 82, 141. Burggraaf, A.J., and Cot, L. (eds) (1996) Fundamentals of Inorganic Membrane Science and Technology, Elsevier. Cheyran, M., and Mehaaia, A. (1986) Membrane, and bioreactors, in Membrane Separation in Biotechnology (ed. W.C. McGregor), Marcel Dekker, New York, p. 255. Coronas, J., Menendez, M., and Santamaria, J. (1994) Methane oxidative coupling using porous ceramic membrane reactors – II. Reaction studies. Chem. Eng. Sci., 49, 2015–2025. Coronas, J., Menendez, M., and Santamaria, J. (1995) Use of a ceramic

membrane reactor for the oxidative dehydrogenation of ethane to ethylene and higher hydrocarbons. Ind. Eng. Chem. Res., 34, 4229–4234. Diakov, V., and Varma, A. (2003) Methanol oxidative dehydrogenation in a packed-bed membrane reactor: yield optimization experiments and model. Chem. Eng. Sci., 58, 801–807. Diakov, V., and Varma, A. (2004) Optimal feed distribution in a packedbed membrane reactor: the case of methanol oxidative dehydrogenation. Ind. Eng. Chem. Res., 43, 309–314. Dittmeyer, R., and Caro, J. (2008) Catalytic membrane reactors, in Handbook of Heterogeneous Catalysis (eds G. Ertl, H. Knözinger, F. Schüth, and J., Weitkamp), Wiley-VCH Verlag GmbH, Weinheim, pp. 2198–2248. Dittmeyer, R., and Reif, M. (2003) Porous, catalytically active ceramic membranes for gas–liquid reactions: a comparison between catalytic diffuser and forced through ﬂow concept. Catal. Today, 82, 3–14. Dittmeyer, R., Höllein, V., and Daub, K. (2001) Membrane reactors for hydrogenation and dehydrogenation processes based on supported palladium. J. Mol. Catal. A: Chem., 173, 135–184. Dixon, A.G. (2003) Recent research in catalytic inorganic membrane reactors. Int. J. Chem. React. Eng., 1, R6. Edgar, T.F., and Himmelblau, D.M. (1989) Optimization of Chemical Processes, Mc Graw-Hill. Eigenberger, G. (1997) Catalytic ﬁxed-bed reactors, in Handbook of Heterogeneous

References Catalysis, vol. 3 (eds G. Ertl, H. Knözinger, and J. Weitkamp), Wiley-VCH Verlag GmbH, Weinheim, pp. 1424–1487. Eigenberger, G., Kolios, G., and Nieken, U. (2007) Thermal pattern formation and process intensiﬁcation in chemical reaction engineering. Chem. Eng. Sci., 62, 4825–4841. Ertl, G., Knözinger, H., Schüth, F., Weitkamp, J. (eds) (2008) Handbook of Heterogeneous Catalysis, vol. 8, Wiley-VCH Verlag GmbH, Weinheim. Fogler, H.S. (1999) Elements of Chemical Reaction Engineering, 3rd edn, Prentice Hall, Upper Saddle River, New Jersey. Froment, G., and Bischoff, K.B. (1979) Chemical Reactor Analysis and Design, John Wiley & Sons, Inc., New York. Gobina, E., Hou, K., and Hughes, R. (1995) Ethane dehydrogenation in a catalytic reactor coupled with a retive sweep gas. Chem. Eng. Sci., 50, 2311–2319. Gryaznov, V.M., Smirnov, V.S., and Mischenko, A.P. (1974) Catalytic reactor for coupled chemical reactions, GB patent 1342869. Haber, J. (1997) Oxidation of hydrocarbons, in Handbook of Heterogeneous Catalysis, vol. 5 (eds G. Ertl, H. Knözinger, and J. Weitkamp), Wiley-VCH Verlag GmbH, Weinheim, pp. 2253–2274. Hamel, C., Thomas, S., Schädlich, K., and Seidel-Morgenstern, A. (2003) Theoretical analysis of reactant dosing concepts to perform parallel-series reactions. Chem. Eng. Sci., 58, 4483–4492. Hamel, C., Bron, M., Claus, P., and Seidel-Morgenstern, A. (2005) Experimental and model based study of the hydrogenation of acrolein to allyl alcohol. Int. J. Chem. React. Eng., 3, A10. Hodnett, B.K. (2000) Heterogeneous Catalytic Oxidation: Fundamental and Technological Aspects of the Selective and Total Oxidation of Organic Compounds, John Wiley & Sons (Asia) Pte Ltd. Itoh, N., Shindo, Y., Haraya, K., and Hakuta, T. (1988) A membrane reactor using microporous glass for shifting equilibrium of cyclohexane dehydrogenation. J. Chem. Eng. Japan, 21, 399–404. Julbe, A., Farrusseng, D., and Guizard, C. (2001) Porous ceramic membranes for

catalytic reactors – overview and new ideas. J. Membr. Sci., 181, 3–20. Kikuchi, E. (1997) Hydrogen-permselective membrane reactors. CATTECH, 1, 67. Kölsch, P., Smekal, Q., Noack, M., Schäfer, R., and Caro, J. (2002) Partial oxidation of propane to acrolein in a membrane reactor-experimental data and computer simulation. Chem. Comm., 3, 465–470. Kragl, U., and Dreisbach, C. (2002) Membrane reactors in homogeneous catalysis, in Applied Homogeneous Catalysis with Organometallic Compounds, 2nd edn (eds B. Cornils and W.A. Herrmann), Wiley-VCH Verlag GmbH, Weinheim, p. 941. Krishna, R. (2002) Reactive separations: more ways to skin a cat. Chem. Eng. Sci., 57, 1491–1504. Kuerten, U., van Sint Annaland, M., and Kuipers, J.A.M. (2004) Oxygen distribution in packed bed membrane reactors for partial oxidation systems and its effect on product selectivity. Int. J. Chem. React. Eng., 2, A24. Levenspiel, O. (1999) Chemical Reaction Engineering, 3rd edn, John Wiley & Sons, Inc., New York. Li, N.N. (2008) Advanced Membrane Technology and Applications, Wiley-VCH Verlag GmbH. Lu, Y.L., Dixon, A.G., Moder, W.R., and Ma, Y.H. (1997a) Analysis and optimization of cross-ﬂow reactors with staged feed policies – isothermal operation with parallel-series, irreversible reaction systems. Chem. Eng. Sci., 52, 1349– 1363. Lu, Y.L., Dixon, A.G., Moder, W.R., and Ma, Y.H. (1997b) Analysis and optimization of cross-ﬂow reactors with distributed reactant feed and product removal. Catal. Today, 35, 443–450. Lu, Y.L., Dixon, A.G., Moder, W.R., and Ma, Y.H. (1997c) Analysis and optimization of cross-ﬂow reactors for oxidative coupling of methane. Ind. Eng. Chem. Res., 36, 559–567. Mallada, R., Menendez, M., and Santamaria, J. (2000) Use of membrane reactors for the oxidation of butane to maleic anhydride under high butane concentrations. Catal. Today, 56, 191–197.

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1 Basic Problems of Chemical Reaction Engineering and Potential of Membrane Reactors Mason, E.A., and Malinauskas, A.P. (1983) Gas Transport in Porous Media: The Dusty Gas Model, Elsevier, Amsterdam. Matros, Y.S., and Busimovic, G.A. (1996) Catalytic processes under unsteady state conditions, Catal. Rev. Sci. Eng., 38, 1–68. Mezaki, R., and Inoue, H. (1991) Rate Equations of Solid-Catalyzed Reactions, University of Tokyo Press. Miachon, S., Perz, V., Crehan, G., Torp, E., Raeder, H., Bredesen, R., and Dalmon, J.-A. (2003) Comparison of a contactor catalytic membrane reactor with a conventional reactor: example of wet air oxidation. Catal. Today, 82, 75–81. Missen, R.W., Mims, C.A., and Saville, B.A. (1999) Introduction to Chemical Reaction Engineering and Kinetics, John Wiley & Sons, Inc., New York. Moulijn, J.A., Makkee, M., and van Diepen, A.E. (2001) Chemical Process Technology, John Wiley & Sons, Ltd, Chichester. Ohlrogge, K., and Ebert, K. (2006) Membranen: Grundlagen, Verfahren Und Industrielle Anwendungen, Wiley-VCH Verlag GmbH, Weinheim. ISBN: 3-527-30979-9. Peinemann, K.-V., and Pereira Nunes, S. (2007) Membrane Technology, Wiley-VCH Verlag GmbH. Pfefferie, W.C. (1966) U.S. Patent App. 3290406. Press, W., Flannery, B., Teukolsky, S., and Vetterling, W.T. (1992) Numerical Recipes, Cambridge University Press. Proceedings of the International Congresses on Catalysis in Membrane Reactors. a) Villeurbanne (1994), b) Moscow (1996), c) Copenhagen (1998), d) Zaragoza (Catalysis Today, 2000, 56), e) Dalian (Catalysis Today, 2003, 82), f) Lahnstein (Catalysis Today, 2005,104), g) Cetraro (11–14 September, 2005), h) Kolkata (18–21 December, 2007), i) Lyon (28 June–2 July, 2009). Sahimi, F. (1995) Flow and Transport in Porous Media and Fractured Rock: from Classical Methods to Modern Approaches, Wiley-VCH Verlag GmbH, Weinheim. Sanchez Marcano, J.G., and Tsotsis, T.T. (2002) Catalytic Membranes and Membrane Reactor, Wiley-VCH Verlag GmbH, Weinheim. Saracco, G., Neomagus, H.W.J.P., Versteeg, G.F., and van Swaaij, W.P.M. (1999)

High-temperature membrane reactors: potential and problems. Chem. Eng. Sci., 54, 1997–2017. Schäfer, R., Noack, M., Kölsch, P., Stöhr, M., and Caro, J. (2003) Comparison of different catalysts in the membranesupported dehydrogenation of propane. Catal. Today, 82, 15–23. Schmidt, L. (1997) The Engineering of Chemical Reactions, Oxford University Press, Oxford. Schramm, O., and Seidel-Morgenstern, A. (1999) Comparing porous and dense membranes for the application in membrane reactors. Chem. Eng. Sci., 54, 1447–1453. Sheintuch, M., and Nekhamkina, O. (2005) The asymptotes of loop rectors. AIChE J., 52, 224–234. Silveston, P.L. (1998) Composition Modulation of Catatlytic Reactors, Gordon and Breach, Amsterdam. Sundmacher, K., and Kienle, A. (eds) (2003) Reactive Distillation, Wiley-VCH Verlag GmbH. Sundmacher, K., Kienle, A., and SeidelMorgenstern, A. (eds) (2005) Integrated Chemical Processes, Wiley-VCH Verlag GmbH, Weinheim. Seidel-Morgenstern, A. (2005) Analysis and experimetnal investigation of catalytic membrane reactors, in Integrated Chemical Processes (eds K. Sundmacher, A. Kienle, and A. Seidel-Morgenstern), Wiley-VCH Verlag GmbH, Weinheim, pp. 359–390. Tellez, C., Menendez, M., and Santamaria, J. (1997) Oxidative dehydrogenation of butane using membrane reactors. AIChE J., 43, 777–784. Thomas, S., Schäfer, R., Caro, J., and Seidel-Morgenstern, A. (2001) Investigation of mass transfer through inorganic membranes with several layers. Catal. Today, 67, 205–216. Thomas, S., Pushpavanam, S., and Seidel-Morgenstern, A. (2004) Performance improvements of parallel−series reactions in tubular reactors using reactant dosing concepts. Ind. Eng. Chem. Res., 43, 969–979. Tonkovich, A.L.Y., Zilka, J.L., Jimenez, D.M., Roberts, G.L., and Cox, J.L. (1996) Experimental investigations of inorganic membrane reactors: a distributed feed

References approach for partial oxidation reactions. Chem. Eng. Sci., 51, 789–806. van de Graaf, J.M., Zwiep, M., Kapteijn, F., and Moulijn, J.A. (1999) Application of a silicalite-1 membrane reactor in metathesis reactions. Appl. Catal. A: Gen., 178, 225–241. Verweij, H. (2003) Ceramic membranes: morphology and transport. J. Mater. Sci., 38, 4677–4695. Vospernik, M., Pintar, A., Bercic, G., and Levec, J. (2003) Experimental veriﬁcation of ceramic membrane potentials for

supporting three-phase catalytic reactions. J. Membr. Sci., 223, 157–169. Wesselingh, J.A., and Krishna, R. (2000) Mass Transfer in Multicomponent Mixtures, Delft University Press. Zaspalis, V.T., and Burggraaf, A.J. (1991) Inorganic Membranes: Synthesis, Characteristics and Applications (ed. R.R. Bhave), Reinhold, New York. Ziaka, Z.D., Minet, R.G., and Tsotsis, T.T. (1993) A high temperature catalytic membrane reactor for propane dehydrogenation. J. Membr. Sci., 77, 221–232.

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2 Modeling of Membrane Reactors Michael Mangold, Jürgen Schmidt, Lutz Tobiska, and Evangelos Tsotsas

2.1 Introduction

As indicated in Chapter 1, different conﬁgurations of membrane reactors can be obtained depending on:

• • •

Placement of the catalyst (tube side, shell side, on the membrane, in a separate layer), Motion, or not, of particulate catalyst (packed beds, ﬂuidized beds), Combination, or not, with electrochemical phenomena.

The present chapter outlines a frame for modeling of mass and heat transfer that is – in principle – common to all these conﬁgurations and accounts for both gas-ﬁlled and porous domains (Section 2.2). After an introduction to key kinetic phenomena (Section 2.3), opportunities for reducing the number of spatial coordinates in the geometrical regions involved are discussed (Section 2.4). Since the systems of model equations are, even after appropriate reduction, not easy to handle, solvability, discretization techniques and fast solvers for large systems of algebraic equations are treated in Section 2.5. Finally, speciﬁc tools used for solving the model equations and, in some cases, also for composing models from fundamental elements and interactions are presented in Section 2.6.

2.2 Momentum, Mass and Heat Balances

Both continuum and discrete (cell, pore-network, etc.) models are common in reaction engineering (Elnashaie and Elshishini, 1993; Tsotsas, 1991). From those two model families, only continuum models are used here in order to describe heat and mass transfer in membrane reactors. Continuum models are universally applicable down to the smallest scale which are signiﬁcant for packed beds and for the operation of micro-reactors. Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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2 Modeling of Membrane Reactors

Since ﬂuid phases and porous regions (membranes, catalyst layers) must be treated simultaneously, multiphase approaches are necessary. In the porous regions themselves, it is possible to distinguish between the ﬂuid and the particulate or solid phases. Several authors have presented calculations with full local resolution of ﬁeld quantities for both ordered and random packed beds (Dixon and Nijemeisland, 2001; Dixon, Nijemeisland, and Stitt, 2003; Manjhi et al., 2006; Tota et al., 2007). However, such solutions are computationally expensive and, hence, seriously limited in regard of the number of particles that can be considered. Therefore, we decided to treat the packed-bed parts of packed-bed reactors (PBR) and packed-bed membrane reactors (PBMR) in a quasihomogeneous way. Consequently, particles and the ﬂuid are summarized to one equivalent phase in every porous region, which is then characterized by porosity (at small tube-to-particle diameter ratios: local porosity) and effective transport coefﬁcients. Irrespective of this approximation, the complete equations for the conservation of momentum, total mass, component mass and energy must be considered in every real (ﬂuid) or assumed (porous) phase. This gives rise to a system of coupled nonlinear partial differential equations of second order, which consists of:

• • • •

The continuity equation, Three equations for momentum transport, for example, the Navier-Stokes equations, The energy balance, (n − 1) species balance equations.

Solution of this system provides the ﬁelds of ﬂow velocity (with the components vr, vϕ, vz, in the case of cylindrical coordinates), pressure p, temperature T, and (n − 1) mass fractions yi for n species components. According to (Bird, Stewart, and Lightfoot, 2002) the differential equations for ﬂuid-ﬁlled regions of the membrane reactor are summarized in tensor form in Table 2.1. The following should be noticed in connection with Table 2.1: Density ρ and enthalpy h can, in general, be obtained from state equations. Here, ideal gas behavior is assumed for all ﬂuid phases. In ideal gases, partial molar volume vi* and molar volume vi of every species are equal to the molar volume of the mixture. It is: 1 vi* = vi = v = , c

(2.1)

n n p n i ρ = ∑ ρi* = ∑ yi ρ = ∑ M iy RT i =1 i =1 i =1

(2.2)

Respective relationships for enthalpy are: i hi , hi* = hi = M h = ∑ hi y i = ∑ y i

(2.3) T

∫ c (T ) dT , h p

i ,ref

(Tref ) = 0.

Tref

Equations 2.7–2.10 are special cases of the general balance:

(2.4)

2.2 Momentum, Mass and Heat Balances Table 2.1

Model equations for the ﬂuid zones, independent from the choice of the coordinate

system. Conservation of total mass ∂ρ + ∇⋅ ( ρv ) = 0 ∂t

(2.7)

Momentum conservation equations ∂ ( ρv ) + ∇⋅ ( ρvv ) + ∇p − ∇⋅ (τ ) − ρ g = 0 ∂t

(2.8)

Transport equations for species ∂ ( ρ yi ) + ∇⋅ ( ρvyi ) + ∇⋅ m iDiff = 0 ∂t

ρ

∂y i + ρv∇yi + ∇⋅ m iDiff = 0 ∂t

(2.9) (2.9a)

Energy conservation equation n ⎞ ∂ ( ρe ) ⎛ + ∇⋅[ v ( ρe + p )] + ∇⋅ ⎜ q + ∑ him iDiff ⎟ − ∇ (τ ⋅ v ) = 0 ⎝ ⎠ ∂t i =1

c pρ

n ⎞ ∂p ∂T ⎛ + c p ρv∇T + ∇⋅ ⎜ q + ∑ him iDiff ⎟ − − v∇p − τ∇v = 0 ⎝ ⎠ ∂t ∂t i =1

(2.10) (2.10a)

With T

e=h−

n p v2 + ; h = ∑ yihi; hi = ∫ c p ,idT ρ 2 i =1 Tref

∂( ρϕ ) + ∇⋅ ( ρϕ v ) + ∇jϕ = sϕ ∂t

(2.11)

(2.5)

for an arbitrary ﬁeld quantity per unit mass of mixture ϕ. At the left-hand side they consider temporal changes in the volume element dV in respect to a ﬁxed coordinate system, convective transport and non-convective ﬂux of the ﬁeld quan tity jϕ . At the right-hand side a source term sϕ (rate of production of ﬁeld quantity per unit volume) is considered. Volume reactions in the ﬂuid phase (homogeneous reactions) are excluded, so that the source term vanishes in the species balances of Table 2.1. For the multi-component systems under consideration the mass average velocity v that corresponds to a mass ﬂux deﬁned as: n n n n ρ* m = ∑ m i = ∑ ρi*ui = ρv , v = ∑ i ui = ∑ yi ui (2.6) ρ i =1 i =1 i =1 i =1 is used as the mixture velocity. Here ui denotes the velocity of component i. The sum of the balances for all species is the continuity equation. Consequently, when using the equation of continuity of total mass of the mixture only (n − 1) species balances are independent from each other.

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2 Modeling of Membrane Reactors

The mass average frame should always be preferred when having to solve not only mass transfer equations, but also the equations of motion. Only in this way is it possible to express the momentum balance for pure ﬂuids and multi-component mixtures in a uniform way according to the principle of conservation of total momentum. The use of other reference velocities, such as the average volume velocity: n u = ∑ ci vi*ui

(2.6a)

i =1

in the so-called Fickian reference system, in general yields signiﬁcantly more complicated expressions for the momentum balance. For ideal gas mixtures it is vi* = 1 c , and the average volume velocity is equal to the average of species velocities: (2.6b) u = ∑ yi ui. Momentum transport by diffusive ﬂuxes has been neglected in Equation 2.8. Without this simpliﬁcation, it would be necessary to treat momentum transport in the same way as mass transport, writing separate balances for the momentum of every individual species (Baranowski, 1975; Kerkhof and Geboers, 2005). However, it is difﬁcult to obtain experimental validation for any method of splitting the pressure and the viscosity tensor down to individual components. Therefore, such a split is reasonable only when the inﬂuence of external force ﬁelds, for example, electrostatic ﬁeld, must be considered. For a multi-component mixture, enthalpy transport by diffusive ﬂuxes has to be accounted for in the energy balance (2.10). Dissipation can be neglected in presence of heat transport for the considered applications and ﬂow velocities. Equation 2.9a for the calculation of molar fraction ﬁelds and Equation 2.10a for the calculation of the temperature ﬁeld are obtained from Equations 2.9 and 2.10 by inserting in them the continuity condition of Equation 2.7 and by inserting additionally a balance of kinetic energy in Equation 2.10. Membrane, membrane-supported catalyst layer and packed bed are regarded – as already mentioned – as quasi-homogeneous phases with the porosity ε. For every such phase an additional system of equations is required, according to Table 2.2. Anisotropy is excluded. Especially for the packed bed, heat and mass transfer limitations between the bulk phase and catalyst particles are neglected. Concerning the porous zones and Table 2.2, the following should be noticed. Velocities denoted by v are superﬁcial velocities that refer to the total crosssectional area or volume of the bed (sum of ﬂuid and particle volume, V = Vf + Vp). Volume ﬂow rate and area yield the average of superﬁcial velocity in any crosssection of the bed: M u = V A and v = . ρf A

(2.17)

Interstitial (or ﬂuid) velocities, which refer only to the volume Vf or area occupied by the ﬂuid, may also be used in porous regions. They are then denoted by vf. The local porosity:

2.2 Momentum, Mass and Heat Balances Table 2.2 Model equations for the porous zones, independent from the choice of the coordinate system.

Conservation of total mass ∂ (ερ f ) + ∇⋅ (ερ f v f ) = 0 ∂t Momentum conservation equations ∂ (ερ f v f ) + ∇⋅ (ερ f v f v f ) + ∇ε p − ∇⋅ (ετ ) − ερ f g = −ε f ∂t Source terms in the momentum conservation equations f = f 1v f + f 2 v f v f

(2.12)

(2.13)

(2.14)

Transport equations for species ∂ (ερ f yi ) + ∇⋅(ερ f v f yi ) + ∇⋅m iDiff = Ri ∂t

(2.15)

Energy conservation equation n n 0 ∂ hR (ερ f e f + (1 − ε ) ρses ) + ∇⋅[ε v f ( ρ f e f + p )] + ∇⋅ ⎛⎜ q + ∑ him iDiff ⎞⎟ − ∇ (ετ ⋅ v f ) = ∑ i i ⎝ ⎠ ∂t i =1 i =1 M i

ε = dV f dV = 1 − (dVs dV )

(2.16)

(2.18)

interrelates superﬁcial and interstitial velocities in the case of isotropic porous media according to this equation: (2.19) v = εv f . Friction and inertial forces caused by ﬂow throughpores lead to an additional loss of momentum – accounted for by the source term f in Equation 2.13. On contrary to the frequently used, simpliﬁed relationship after (Forchheimer, 1901): ∇p = − f 1 v − f 2 v v (2.20) Equation 2.13 takes into consideration all kinds of momentum transport, especially viscous transport in the ﬂuid. The limiting case of f2 = 0, which is always applicable to the membrane and membrane-supported catalyst layers, corresponds to Darcy’s law. For the packed bed, the coefﬁcients f1 and f2 are calculated according to (Ergun, 1952): f 1 = 150

(1 − ε )2 η f (1 − ε )2 ρ f , f = 1 . 75 . 2 ε 3 d p2 ε 3 dp

(2.21)

This is done on the basis of local values of porosity after (Hunt and Tien, 1990): ⎛ R −r⎞ ε (r ) = ε ∞ + (1 − ε ∞ ) exp ⎜ −6 ⎝ d p ⎟⎠

(2.22)

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2 Modeling of Membrane Reactors

Heterogeneous catalytic reactions appear now in the source term Ri of the species balances. This can be expressed as: nr

i ∑ ν ij (1 − ε ) ρcat * r j with ρcat * = Ri = M j =1

M cat Vs

(2.23)

In the case of packed beds, the volume of the solid phase Vs is given by the volume of the particles. The molar rate of reaction j, rj, refers here to the mass of catalyst used. Component adsorption and desorption on the solid phase are neglected in relation to the accumulation term. In the energy balance, the heat capacity of the solids, which ﬁll (1 − ε) of the space, is considered. Local thermal equilibrium is assumed between solids and the ﬂuid. A source term accounts for reaction enthalpies, where hi0 is the molar enthalpy of formation of species i. Since tubular reactors are used in most applications, axisymmetric conditions can be assumed. This saves much computational time in comparison to 3-D calculations. The 2-D equations resulting in cylindrical coordinates using the z-axis as a rotation axis are exemplarily summarized for porous domains in Table 2.3.

Table 2.3

Model equations for the porous zones in 2-D axisymmetric geometry.

Conservation of total mass ∂ (ερ f ) ∂ (ερ f v z , f ) ∂ (ερ f vr , f ) ερ f vr , f + + + =0 ∂t ∂z ∂r r

(2.24)

Momentum conservation equations z-coordinate: ∂ (ερ f v z , f ) ∂ (ερ f v z , f v z , f ) 1 ∂ (rερ f vr , f v z , f ) ∂ (ε p ) + + + − r ∂t ∂z ∂r ∂z ∂ 1 ∂ (ετ zz ) − (rτ rz ) − ρ f g z = −ε ( f 1v z . f + f 2 v f v z , f ) r ∂r ∂z

(2.25)

r-coordinate: ∂ (ερ f vr ,v ) ∂ (ερ f vr , f v z , f ) 1 ∂ (rερ f vr , f vr , f ) ∂ (ε p ) + + + − r ∂t ∂z ∂r ∂r ∂ 1 ∂ (ετ rz ) − (εrτ rr ) − ερ f g r = −ε ( f 1vr , f + f 2 v f vr , f ) r ∂r ∂z

(2.26)

Transport equations for species ∂ 1 ∂ (rερ f vr , f yi ) ∂ (ερ f v z , f yi ) 1 ∂ ∂m Diff + + (ερ f yi , f ) + (rm iDi,riff ) + i ,z = Ri ∂r ∂z ∂t ∂z r r ∂r

(2.27)

Energy conservation equation ∂ 1 [ ∂rvr , f (ερe f + p )] ∂ [ v z , f (ερe f + p )] ⎡ 1 ∂ ∂q (rqr ) + z ⎤ + + + (ερ f e f + (1 − ε ) ρses ) + ⎣⎢ r ∂r r ∂r ∂z ∂t ∂z ⎦⎥ Difff n ∂ ετ + ετ v v ( hi0Ri 1 1 ∂ ∂ ∂ h m zz z , f rz r , f ) ⎤ ⎡ i i ,z ⎤ ⎡ Diff = ∑ ⎢⎣ r ∂r (rhim i ,r ) + ∂z ⎥⎦ + ⎣⎢ r ∂r (rε (τ rr vr , f + τ rz v z , f )) + ⎦⎥ i =1 Mi ∂z

(2.28)

2.3 Transport Kinetics

Apart from the system of governing differential equations, it is necessary to have:

• •

A precise deﬁnition of control volume (solution domain), An adequate selection of boundary conditions.

These are outlined in Section 2.4. Before that, kinetic expressions needed in order to calculate the ﬂuxes in the governing equations are discussed.

2.3 Transport Kinetics 2.3.1 Fluid-Filled Regions

Comprehensive treatments of diffusion in multi-component mixtures have been provided by, among others, (Haase, 1963; de Groot and Mazur, 1984; Taylor and Krishna, 1994; and Cussler, 1997). Appropriate simpliﬁed approaches are used in the present work. Cross-effects like thermal diffusion or interrelation between reaction and momentum transport and the inﬂuence of external force ﬁelds are neglected. It should be noticed that kinetic equations have a similar structure for all transport processes, correlating the ﬂux of momentum, mass and energy with relevant driving forces, which are gradients of, respectively, velocity, chemical potential and temperature in the assumed continuum. 2.3.1.1 Molecular Transport of Momentum The kinetics of molecular transport of momentum is described in a linear way by the generalized form of Newton’s law of viscosity. Taking into account that the shear stresses are a symmetric combination of velocity gradients and that the ﬂuid is isotropic, it follows after (Bird, Stewart, and Lightfoot, 2002):

(

)

2 τ = η (∇v + ∇v t ) − η − κ (∇⋅ v )I 3

(2.29)

The quantity κ in Equation 2.29 is called the dilatational viscosity. It can be neglected for low density gases at low Mach number ﬂows. 2.3.1.2 Heat Conduction The law of heat conduction, also known as Fourier’s law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the cross-sectional area to that gradient. Deﬁned per ﬂow area, the heat ﬂux can be calculated as: q = − λ∇T (2.30)

Cross-effects described by the thermodynamics of irreversible processes are neglected. The thermal conductivity λ corresponds to the molecular quantity λg in the gas phases and in the porous media to the effective value λeff.

35

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2 Modeling of Membrane Reactors

2.3.1.3 Molecular Diffusion The mentioned assumption that the inﬂuence of external force ﬁelds and all crosseffects foreseen in general irreversible thermodynamics can be neglected leads to the Stefan–Maxwell equations (Taylor and Krishna, 1994): n y i y j (u i − u j ) yi (∇μi )T , p = −∑ (2.31) RT DijM j =1

for describing diffusion in multi-component mixtures. The derivation of these equations is based on momentum transfer during collisions between different species. Equation 2.31 is independent from the average velocity of the mixture and uses gradients of chemical potential μi as the driving forces of mass transport. These gradients vanish at equilibrium. By deﬁnition of molar diffusion ﬂuxes in respect to the average component velocity (2.6b): n n iDiff = n i − ci u = ci (ui − u ) , ∑ n iDiff = 0

(2.32)

i =1

the dependence between ﬂuxes and driving forces follows from Equation 2.32 to: n Diff y j ni − yi n Diff ci j (∇μi )T , p = −∑ (2.33) M RT D ij j =1 Alternatively, the relationships: n m iDiff = m i − ρi v = ρi* (ui − v ) , ∑ m Diff = 0

(2.34)

i =1

M y j m iDiff − i yi m Diff j Mj ρi* ( ∇μi )T , p = −∑ RT DijM j =1 n

(2.35)

are obtained by using mass-average velocity (2.6) and mass-related diffusion ﬂuxes. It should be noticed that with n components (n − 1) Equations 2.33 and 2.35 are independent from each other. A clear disadvantage when computing with the Stefan–Maxwell equations is that the diffusion ﬂuxes can not be expressed explicitly. Matrix formulation according to (Taylor and Krishna, 1994) in the form:

c

B −1 ∇μ = −c [B −1 ][ Γ ](∇y ) (n ) = − RT [ ][ ]

(2.36)

with: Bii =

n yi y 1 ⎞ ⎛ 1 + ∑ Mi , Bij = − yi ⎜ M − M ⎟ M ⎝ Dij Din ⎠ Din j =1 Dij j ≠i

(2.37)

does not remove this disadvantage. Here [Γ] is a matrix that should be calculated from activities in order to – when necessary – account for real mixture behavior.

2.3 Transport Kinetics

Friendlier for calculations are the generalized expressions according to Fick, which provide explicitly the diffusion ﬂuxes as: n −1 n iDiff = −c ∑ Dij ∇y j

(2.38)

j =1

or: n −1 m iDiff = − ρ ∑ Dij* ∇y j

(2.39)

j =1

The disadvantage of these expressions is a relatively strong dependence of the multi-component diffusion coefﬁcients Dij or Dij* upon the composition of the mixture. A further simpliﬁcation is to use pseudo-binary diffusion coefﬁcients Dipb and relate the ﬂux of every species i to the driving force ∇yi of only this component: ipb ∇yi n iDiff = −cD (2.40) However, if one requires the independence of diffusion coefﬁcients from driving forces, the relationship: n

Diff

∑ n i =1

i

n

n

i =1

i =1

= −c ∑ Dipb ∇yi = −c ∑ (Dipb − Dnpb )∇yi = 0

(2.41)

is obtained. This leads immediately to: Dipb = Dnpb

i = 1, 2, … , n − 1.

(2.42)

Equation 2.42 means that all diffusion coefﬁcients Dipb should have the same value, which is obviously not true in multi-component mixtures. A comprehensive discussion of the complex interrelations between diffusion coefﬁcients deﬁned in different ways for multi-component mixtures is given by (Wesselingh and Krishna, 2000). Fortunately, ideal gas behavior can usually be assumed. Additionally, for the membrane reactors under consideration it can be assumed that every species i ≠ n is present in strong dilution to the inert component n. Signiﬁcant simpliﬁcations are possible on this basis. From the deﬁnition of the chemical potential of ideal gases it follows: n −1 n −1 yi (∇μi )T , p = ∑ Γ ij ∇y j = ∑ ∇y j RT j =1 j =1

(2.43)

For diluted mixtures with (at the limit): yi ≠ n = 0, yn = 1

(2.44)

Equation 2.39 simpliﬁes (Taylor and Krishna, 1994), leading to multi-component diffusion coefﬁcients of: Dij = 0 and Dii = DinM

i = 1, 2, … , n − 1

(2.45)

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2 Modeling of Membrane Reactors

in Equation 2.45. These diffusion coefﬁcients can be calculated according to (Fuller, Schettler, and Giddings, 1966) – as recommended by (Reid, Prausnitz, and Sherwood, 1977) – by means of the equation:

Din = 1.013⋅10 −7 T 1.75

i +M n ⎞ ⎛M ⎜ ⎟ M M ⎝ i n ⎠ p ⎡⎣( ∑ v )i

0.333

+ ( ∑ v )n

0.333 2

⎤ ⎦

(2.46)

(T in K, p in bar, Din in m2/s). The so-called diffusion volumes (∑ν)i are found for each component by summing of the atomic and structural increments and can be taken from (Poling, Prausnitz, and O’Connell, 2001) or (Lucas and Luckas, 2002). Because of inaccuracies of modeling and computation, the sum of diffusion ﬂuxes is never exactly equal to zero: n (2.47) ∑ m iDiff = m cor ≠ 0. i =1

To still guarantee the conservation of mass and fulﬁll Equations 2.32, 2.34 either all ﬂuxes must be adjusted by weighted application of some correction terms, or the main mixture component must be ﬁtted. In our case it is reasonable to implement the correction in the excess component (inert species n): Diff n − m cor. m nDiff (2.48) ,cor = m Mass-average velocity v, the composition ﬁelds obtained from the (n − 1) independ ent material balances and the diffusion ﬂuxes m i ,i ≠ n have to be treated correspondingly in the course of numerical calculations. The correction of diffusion ﬂuxes is especially important in the case of creeping ﬂow as well as for closure of the material balances over the entire computational domain. 2.3.2 Porous Domains

In literature it is usual to distinguish between macro-pores (dpore > 50 nm), mesopores (2 nm < dpore < 50 nm) and micro-pores (dpore < 2 nm) and to classify porous materials correspondingly (Melin and Rautenbach, 2007). This classiﬁcation does not say anything about the prevailing transport mechanisms, because it does not put the pore diameter dpore in relation to the size of the transported species dmol and to the free mean path of gas molecules l. By introducing these quantities and the Knudsen number Kn = l/dpore we can better recognize regions of:

• • •

Molecular diffusion or viscous ﬂow, when l < dpore (Kn < 1), Knudsen diffusion, when dmol < dpore < l (Kn > 1), Conﬁgurational diffusion (molar sieving effect), when dmol ≈ dpore.

The mentioned transport mechanisms are illustrated in Figure 2.1 and are brieﬂy explained in the following – with the exception of conﬁgurational diffusion, which is not of interest for the used gases and porous media.

2.3 Transport Kinetics

free diffusion Figure 2.1

viscous flow

Knudsen diffusion

molecular sieving

Transport mechanisms in porous media.

2.3.2.1 Molecular Diffusion Molecular (or free) diffusion is dominated by the interactions between gas molecules and, thus, prevails when the pore diameter is considerably larger than the mean free path. If collisions with the wall can be completely neglected, the total momentum of the molecules remains constant. Mass transport kinetics can be modeled as previously explained. Diffusivities are, however, reduced in a porous medium by a factor of F0, which is often expressed as the ratio between porosity ε and tortuosity τ. This gives rise to effective diffusion coefﬁcients:

ε Dije = F0Dij = Dij τ

(2.49)

2.3.2.2 Knudsen Diffusion When the pore diameter is comparable to or smaller than the mean free path, momentum is transferred primarily by collisions of molecules with the wall. Gas– wall interactions dominate, and molecules of different species are transported independently of each other, corresponding to their mobility. By application of kinetic gas theory to a single, straight and cylindrical pore the coefﬁcient of Knudsen diffusion can be derived to:

1 8RT DK ,i = dpore i πM 3

(2.50)

For a porous medium, a more general form of this equation can be used, namely: ε dpore 4 8RT DK ,i = K 0 ,K = i 0 τ 4 πM 3

(2.51)

By analogy to molecular diffusion, the Knudsen diffusion ﬂux can be calculated to: ε DK ,i n iK = ∇pi τ RT The gradient of partial pressure is the driving force of the process.

(2.52)

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2 Modeling of Membrane Reactors

2.3.2.3 Viscous Flow A total pressure gradient gives rise to mass transport by convective, viscous ﬂow. Both molecular diffusion and viscous ﬂow gradually disappear when moving into the Knudsen region. Though viscous ﬂow does not contribute to the separation of different species, its role may be very important in membrane reactors. For a single capillary, viscous ﬂow can be calculated according to Hagen and Poiseuille (Jackson, 1977). Due to laminar conditions, average velocity is directly proportional to the pressure gradient. A modiﬁed version of the Hagen–Poiseuille law that goes back to Darcy can be used for porous media, leading to a ﬂux of:

n iv = −

1 B0 p∇p η RT

(2.53)

with: B0 =

2 ε dpore . τ 32

(2.54)

For the convective ﬂow of a mixture it follows: n

n v = ∑ n iv.

(2.55)

i =1

2.3.2.4 Models for Description of Gas Phase Transport in Porous Media According to Jackson – and based on ideas that go back to Clerk Maxwell – porous media can be considered as either networks of interconnected capillaries or assemblies of stationary obstacles dispersed in the gas at a molecular scale for modeling mass transport. Models of the ﬁrst type can be closely related to the real structure of the medium, but have some difﬁculties in implementing the Knudsen effect. A prominent representative of models of the second type is the dusty gas model (DGM), which was rediscovered independently three times by (Deriagin and Bakanov, 1957; Evans, Watson, and Maso, 1962; Mason, Malinauskas, and Evans, 1967; and Mackey, 1971). The model considers the porous medium as composed of giant molecules that are ﬁxed and uniformly distributed in space. These socalled dust particles are treated as one additional component of the gas mixture in the frame of a Stefan–Maxwell approach. By consequence, Knudsen diffusion is automatically accounted for as a result of molecule–dust interactions. In contrast, the porous medium is represented by formal parameters in the model, which are denoted by F0, K0, B0 in the foregoing discussion. To connect these parameters with characteristic geometrical features of the medium (like the mentioned ratio of porosity and tortuosity, and the mean pore diameter) additional assumptions are required. Micro-structural characteristics get lost, in the same way as heterogeneities at the macro-scale. Figure 2.2 illustrates the combination of molecular diffusion and Knudsen diffusion with viscous ﬂow in the DGM by an electrical analog. According to it, the total ﬂux is split into parallel paths of diffusion and viscous ﬂow:

n i = n iD + yi n v

(2.56)

2.3 Transport Kinetics

molecular diffusion

Knudsen diffusion

n˙ D i

total flux n˙ i

n˙ i + d˙n i viscous flow

n˙ vi

Figure 2.2

Electrical analog illustrating transport phenomena in porous media.

Molecular diffusion and Knudsen diffusion are combined in series. This corresponds to the law of (Bosanquet, 1944) for an overall diffusion coefﬁcient of: Di ,eff =

1 1 − ayi 1 + Dije DK ,i

(2.57)

The parameter α in Equation 2.57 takes into account the ratio of molar ﬂuxes or, according to Graham’s law (Evans, Watson, and Maso, 1962), the ratio of the square root of the molar masses of the considered components:

α =1−

j M n i =1− i n j M

(2.58)

In the case of equimolar diffusion, the transported amounts of different species are equal to each other. Hence, α = 0 and Equation 2.57 can be reduced to the form: Di ,eff =

1 1 1 + Dije DKi

(2.59)

Based on the assumptions of spatially uniform dust concentration, motionless dust (such that n n+1 = 0) and very massive dust molecule (Mn+1 → ∞) equations describing the dusty gas model can be obtained. A concise form of these equations is: p dyi y ⎛ B p ⎞ dp + i ⎜1 + 0 ⎟ = dr RT ⎝ ηDK ,i ⎠ dr RT

yi n j − y j n i n − i DK ,i Dije j = 1 ,i ≠ j n

∑

(2.60)

A matrix formulation that is more convenient for numerical calculations reads: n = − Cii =

1 −1 C F, RT

n y 1 y + ∑ ie ; Cij = ie , Dij DK ,i i =1, j ≠1 Dij

B p ⎞ ⎛ Fi = p∇yi + yi ⎜ 1 + 0 ⎟ ∇p ⎝ ηDK ,i ⎠

(2.61)

41

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2 Modeling of Membrane Reactors

The dusty gas model can be extended to include thermal diffusion effects, nonideal ﬂuid behavior, external body forces, surface diffusion and selective viscous ﬂow. Criticism to the DGM concerns especially the accounting of the viscous contribution (Kerkhof and Geboers, 2005; Krishna and van Baten, 2009).

2.4 Reduced Models

Depending on the number and kind of zones (domains), the models discussed in the foregoing sections can be adapted for simulating three different types of reactors, namely:

• • •

Conventional packed-bed reactor (PBR), Packed-bed membrane reactor (PBMR), Catalytic membrane reactor (CMR).

A PBR consists only of the catalyst-ﬁlled tube side. In a PBMR, the membrane separates the tube side from the shell side. One of them is empty, and the other (usually the tube side) is ﬁlled with catalyst particles. In a CMR both sides are empty, because the membrane itself has a catalytically active layer. For the description of different reactors and conditions, transformations of model equations are necessary. Models of different spatial dimensionality in the treatment of the considered domains have been used, such as:

• • • •

1-D PBMR (membrane not modeled) 1-D + 1-D (membrane in r-direction, channels in z-direction) 2-D PBMR (membrane not modeled) 2-D CMR (membrane, tube side, shell side)

To completely specify the model used for a certain mode or operation, it is necessary to go through several steps:

• • • •

Identiﬁcation of the domains that need to be modeled, Selection of the spatial dimensionality of equations for each domain, Introduction of appropriate kinetic expressions into the balance equations, Deﬁnition of all necessary boundary conditions.

For reasons of space, it is not possible to provide here a comprehensive set of equations for all operational modes that have been modeled. Every speciﬁc implementation is explained in the following chapters, as it comes to use. However, the procedure should be illustrated by one example, speciﬁcally the example of CMR modeling. The complete CMR model is based on the standard consideration of convective and diffusive transport taking into account the necessary source and sink terms. Because of the symmetry conditions in the tube geometries, it is possible to model each zone of the membrane reactor in a 2-D way without information loss. Because of the multi-dimensional modeling, the heat and mass transfer between the zones are integral parts of the model and no correlations for Nusselt or Sherwood

2.4 Reduced Models

numbers are needed (Georgieva et al., 2005). The simulated axisymmetric geometry is presented in Table 2.4. The same table summarizes the steady-state balance equations for the catalytic active membrane, model assumptions and the boundary conditions for the entire computational domain. The model description of the empty channels is not presented in Table 2.4, but it can be derived from the equations for the catalytic active zone by removing the source terms and by replacing the effective transport coefﬁcients with molecular values. Because of the small geometrical dimensions, laminar ﬂow conditions are assumed and plug ﬂow proﬁles are deﬁned at the reactor inlets. The inﬂuence of gravitation can also be neglected in gas systems. The pressure drop through each membrane layer is considered by means of a sink term in the momentum equations. The parameters f1 and f2 are calculated using the coefﬁcients determined by application of the DGM: f1 =

ηN2 , DK ,N2 ηN2 B0 + p

f 2 = 0, B0 =

2 4 8RT ε dpore ε dpore , DK ,N2 = K 0 , K0 = N2 3 τ 32 πM τ 4

(2.62)

These expressions are derived from the DGM for the transport of N2 through the membrane and take into account the viscous slip at the pore walls. At very small Knudsen numbers, the laminar viscous ﬂow of a single species is known as Poiseuille ﬂow. In this particular case, the non-slip boundary condition can be used reliably. Viscous slip is observed in the region of Knudsen diffusion and in the transition region, that means for Kn > 0.1 (Young and Todd, 2005). Because the developed model for description of the porous media is pseudo-homogenous, the viscous slip on the pore walls can be expressed only by integral and apparent quantities. The parameter f2 was set to zero due to the laminar character of the ﬂow. The investigated membranes have an asymmetric structure. The experimentally determined parameters of each membrane layer (see Chapter 4) are used for the deﬁnition of the sink terms in the momentum equations and for the calculation of transport coefﬁcients. In CMR, the reactions take place only in the catalyst layer. Therefore, the reaction terms are considered in the conservation equations for mass and energy only in this zone. To apply the experimentally determined reaction kinetics, the reaction constants have to be converted for the coated vanadium amount in the catalyst layer on the basis of the Turnover number (Masel, 2001). Because of the strong dilution of the educts, the material properties are based on correlations for nitrogen. Therefore, a quasi-binary gas mixture was assumed for the calculation of diffusion coefﬁcients, in which each species is located only in nitrogen environment. The effective diffusion coefﬁcients are calculated according to Equation 2.59. The determination of effective thermal conductivity are discussed in Chapter 4. For a closed solution of the equation system, appropriate boundary conditions are needed. At the channel entrances, the total mass ﬂow rates, the mass fractions of n − 1 components and the initial temperature have to be deﬁned. Additionally, the operating pressure has to be speciﬁed and set as a boundary condition at the reactor outlet. On this basis, the pressure drops through the packed bed,

43

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2 Modeling of Membrane Reactors Table 2.4 Model equations for the catalytical membrane layer.

Model assumptions: Steady state, laminar, pseudo-homogeneous, extended Fickian law, highly diluted reaction system, no homogeneous reaction, plug ﬂow proﬁles at reactor inlets, no gravity inﬂuence Conservation of total mass:

∂ ( ρ f v z ) ∂ ( ρ f vr ) ρ f vr + + =0 r ∂z ∂r Momentum conservation equations z-Coordinate:

(

(

(

)

))

(

)

∂ ( ρ f v z v z ) 1 ∂ (rρ f vr v z ) ∂p ∂ ⎡ ∂v 2 ∂v z ∂v r v r ⎤ 1 ∂ ⎡ ∂v z ∂v r ⎤ − = − f 1v z η 2 z− + + rη + − + + r ∂z ∂r r ⎥⎦ r ∂r ⎢⎣ ∂r ∂z ∂z ⎢⎣ ∂r ⎥⎦ ∂z 3 ∂z ∂r r-Coordinate:

(

(

))

∂ ( ρ f vr v z ) 1 ∂ (rρ f vr vr ) ∂p ∂ ⎡ ∂vr ∂v z ⎤ 1 ∂ ⎡ ∂v 2 ∂v z ∂v r v r ⎤ − rη 2 r − = − f 1vr η + + − + + + r ∂z ∂r ∂r 3 ∂z ∂r r ⎦⎥ ∂r ∂z ⎣⎢ ∂z ∂z ⎦⎥ r ∂r ⎣⎢

membrane or empty channels are calculated. The gradient of the axial component of the velocity vector is set to zero at the axis of the tube, where the radial velocity is also zero. Adiabatic boundary conditions are applied at the reactor walls, so that heat and mass streams are vanishing there. Model development, reduction, implementation and solution can be organized and supported with the help of modern computational tools, as discussed in the following.

2.5 Solvability, Discretization Methods and Fast Solution

As seen in the previous sections the modeling of membrane reactors leads to a coupled system of nonlinear partial differential equations completed by appropriate boundary and initial conditions. The solvability of these types of initial boundary value problems is not at all a trivial problem and even in special situations

2.5 Solvability, Discretization Methods and Fast Solution Table 2.4

(Continued)

Transport equations for species:

(

) (

)

nr 1 ∂ (rρ f vr yi ) ∂ ( ρ f v z yi ) 1 ∂ ∂y ∂ ∂y i + ρ f Di ,efff i = Mi ∑ ν ij(1 − ε )ρcatr j + + rρ f Di ,eff ∂r ∂z r r ∂r ∂z ∂z ∂z i =1

Energy conservation equation:

( ) ( )

)

1 ∂ [rvr ( ρe f + p )] ∂ [ v z( ρe f + p )] ⎡ 1 ∂ ∂ ∂T ⎤ ∂T + + + + rλ e rλ e ⎣⎢ r ∂r ∂r ∂z r ∂z ∂z ⎦⎥ ∂r n nr ⎡ 1 ∂ rh ρ D ∂yi + ∂ h ρ D ∂yi ⎤ = h 0 ν (1 − ε ) ρ r i f i , eff cat j ∑ i ∑ ij ⎢⎣ r ∂r i f i ,eff ∂r ∂z ∂z ⎥⎦ i =1 i =1

(

) (

Boundary conditions: Geometric position Tube side, z = 0 Shell side, z = 0 Tube side, z = L

Momentum balance TS,0 M SS,0 M pTS = p0

Shell side, z = L Axis, r = 0 Interiors, ∀r j Walls

Mass balance yi,TS,0 yi,SS,0

Energy balance TTS,0 TSS,0

νz,SS = 0, νr,SS = 0,

∂yi ,SS ∂yi ,SS = 0, =0 ∂r ∂z

∂TSS ∂TSS = 0, =0 ∂r ∂z

∂v z , TS = 0, vr , TS = 0 ∂r

∂yi,TS =0 ∂r

∂TTS =0 ∂r

p j = p j +1,

∂vrj ∂vrj +1 = ∂r ∂r

νz = 0, νr = 0

y ij = yij +1,

∂yij ∂yij +1 = ∂r ∂r

∂y i ∂y i = 0, =0 ∂r ∂z

T j = T j +1,

∂T j ∂y j + 1 = ∂r ∂r

∂T ∂T = 0, =0 ∂r ∂z

is the subject of current mathematical research, for example, see (Lions, 1996; Galdi, 1994; Girault and Raviart, 1986; Amann, 2001; Russo and Simader, 2006; Zajaczkowski, 2007). In general there are no classic solutions, that is, solutions which are continuously differentiable, and one has to reformulate the partial differential equations in a so-called weak form for which the existence of weak solutions can be established. Without going into the mathematical details let us summarize some existence and uniqueness results for a ﬂow problem described by the incompressible Navier–Stokes equations in a bounded domain Ω: ∂v 1 Δv = f , ∇⋅ v = 0, in Ω, v = vb on ∂Ω, v t = 0 = v0 (2.63) + ∇⋅ ( v ⊗ v ) + ∇p − Re ∂t In the two-dimensional case, the Navier–Stokes equations with given velocity ﬁeld vb at the boundary ∂Ω of the domain have, on any time interval [0, te], a unique solution that is also a classic solution provided that all data of the problem are smooth enough. But in the three-dimensional case, the existence of such solu tions has been proved only for sufﬁciently small data v0 , vb , f or on sufﬁciently short intervals of time (Lions, 1996). The existence of weak solutions for the stationary Navier–Stokes equations can be guaranteed in both the two- and three-dimensional

45

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2 Modeling of Membrane Reactors

cases, but uniqueness has not been proved for all data and all Reynolds numbers; in particular a smallness condition on the data is required which for ﬁxed f and vb results in an upper bound for the Reynolds numbers (Galdi, 1994). Another delicate question is the correct formulation of boundary conditions since a prescribed velocity proﬁle – as in the mentioned solvability results above – seems to be questionable, at least at the outﬂow part of the boundary. A discussion of this issue and its numerical aspects can be found in (Sani and Gresho, 1994). A possible analytical approach to handle this situation can be found in (Kracmar and Nestupa, 2001). In the following, we assume that solutions of the underlying partial differential equations with certain smoothness properties do exist. Only in very special cases and simple domain geometries, like for example the channel ﬂow of an incompressible ﬂuid with no slip boundary condition at the walls and a prescribed parabolic in- and outﬂow boundary condition, are the Hagen–Poiseuille ﬂow, analytical expressions for the solutions of the Navier–Stokes equations available. Therefore, analytical and/ or numerical approximations of solutions play an essential role. In general the solution of the partial differential equation depends on some dimensionless parameters like the Reynolds, Péclet, Damköhler, or some other numbers. If we are looking for solutions in cases where these parameters achieve very large or small values the method of matched asymptotic expansions can often be applied (Eckhaus, 1973; Varma and Morbidelli, 1997). It is based on the solution of the reduced problem by setting the corresponding parameter equal to the limit case and correcting the reduced solution in order to fulﬁll the remaining conditions which could not yet be satisﬁed. The correction solves a simpliﬁed local problem generated by a proper scaling and tending the parameter again to the limit. As a result of the matched asymptotic expansion method an analytical approximation of the solution is available where the accuracy depends on how close the parameter is to the limit. If the reduced and/or the local problem cannot be solved analytically, the subproblems can also be approximated numerically. An example of this approach is given in Chapter 4. In most cases, however, it is hopeless to look for analytical approximations. Then, one has to discretize the partial differential equations. Among the numerical schemes ﬁnite difference, ﬁnite volume or ﬁnite element methods are most popular. In computational ﬂuid dynamics (CFD), discretizations by ﬁnite volume (FVM) and ﬁnite elements (FEM) are common due to their ﬂexibility to adapt to the geometry of the computational domain. In ﬁnite volume methods, the computational domain is subdivided into control volumina (cells) and an integral form of the balance equations is derived by integration over theses cells. Then, in each cell we look for values of the solution of the problem at the barycentre (cell-centered FVM) or at the vertices (cell-vertex FVM). An important problem is the discretization of convective terms which for the standard cell-centered FVM consists of: ∫ ∇⋅( ρϕ v )dV = ∫ ρϕ v ⋅ndA ≈ {ρuA}e{ϕ }e − {ρuA}w {ϕ }w + {ρvA}n{ϕ }n − V

A

{ρvA}s {ϕ }s + {ρwA}t {ϕ }t − {ρwA}b{ϕ }b

with v = (u , v, w )

(2.64)

2.5 Solvability, Discretization Methods and Fast Solution

where V denotes the control volume, A its boundary. The values of the quantities on the east, west, north, south, top and bottom parts of the boundary are expressed by linear interpolation from the neighboring cells. However, it turns out that the resulting difference scheme becomes unstable in the case of dominated convection, that is, at high Reynolds numbers. Therefore, instead of using linear interpolation to evaluate the value of ϕ on a boundary part of A, the value of ϕ at the next upwind cell is taken, which corresponds more strongly to the physics of the problem and leads to a stable discretization. When solving incompressible ﬂow problems with a cell-centered FVM for velocity and pressure on the same grid of control volumina unphysical oscillations may appear. To overcome this type of instability staggered grid methods can be used, in which the control volumina for the velocity components and the pressure do not coincide (Noll, 1993). However, on general non-orthogonal grids the staggered grid approach becomes costly due to the need of using grid-oriented components of vectors and tensors (Ferziger and Peric, 1996). Improved pressure–velocity coupling algorithms based on special interpolation formulas on the cell boundaries have been developed to allow also non-staggered grids and to avoid unphysical oscillations of the pressure (Noll, 1993; Ferziger and Peric, 1996). The discretization of the convective and diffusive terms of the transport equations by FVM is conservative which means that the sum of in and outgoing mass ﬂuxes over a cell is equal to zero. This property is an essential advantage compared to ﬁnite differences. However, it is difﬁcult to extend and analyze FVM to higher than ﬁrst order. Finite element methods are based directly on the weak formulation of the problem which is also used to investigate the existence and uniqueness of solutions. For them most mathematical tools are available, even the convergence properties of FVM are analyzed by tools developed for FEM (Chou and Ye, 2007). Using higher-order polynomials in FEM any approximation order can be achieved provided that the solutions of the partial differential equations are smooth enough. Another option for increasing the accuracy of ﬁnite element solutions is to take proﬁt from superconvergence properties, that is, that the error to the interpolation is of a higher order than the error to the solution itself. A proper postprocessing for the computed ﬁnite element solutions allows recovery of this higher order (Matthies, Skrzypacz, and Tobiska, 2005). Examples of this technique are given in Chapter 4. Instabilities caused by dominated convection can be handled for low-order ﬁnite element approximations again by upwinding (Tabata, 1977). Unfortunately, as in FVM, upwinding has the tendency to smear out sharp layers of the solution. Therefore, starting in the 1980s new mathematical approaches have been developed which are able to suppress oscillations caused by dominated convection and can be applied to any order of ﬁnite elements (Brooks and Hughes, 1982). The streamline-upwind Petrov–Galerkin (SUPG) method consists in adding weighted residuals of the differential equation to the standard ﬁnite element method. Other approaches, like the Galerkin least square (GLS) and the residual free bubble (RFB) method have been suggested and analyzed. All these approaches fall into the class of stabilized ﬁnite element methods in which the recently

47

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2 Modeling of Membrane Reactors

Figure 2.3

Examples of inf-sup stable ﬁnite element pairs.

developed stabilization by local projection (LPS) (Matthies, Skrzypacz, and Tobiska, 2007; Ganesan, Matthies, and Tobiska, 2008) seems to be most attractive since it allows to attain the same stability as the SUPG method (Knobloch and Tobiska, 2008) but with less computational costs and in an symmetric manner which is important for optimization. Note that, in particular for higher-order ﬁnite elements, stabilized methods do not remove oscillations completely; but in contrast to standard ﬁnite element methods they are strongly localized to the regions where there are sharp layers in the solution. Adaptive mesh-reﬁnements in these regions or additional tools like shock capturing techniques can try to improve the remaining situation. The mass conservation in FEM is in contrast to FVM not automatically guaranteed, however the use of discontinuous pressure approximations in incompressible ﬂow computations can considerably improve the fulﬁllment of the incompressibility constraint. Moreover, for coupled ﬂow–transport problems advanced ﬁnite element methods are available (Matthies and Tobiska, 2007). As in FVM (where staggered grids or special interpolations have been used to solve the Navier–Stokes equation) a compatibility condition between the ﬁnite element spaces approximating velocity and pressure is needed to avoid non-physical oscillations in the pressure ﬁeld. This phenomenon is well understood and results in the use of inf-sup stable ﬁnite element1) pairs for velocity and pressure (Girault and Raviart, 1986; Brezzi and Fortin, 1991). For example, continuous, piecewise quadratic functions for both the velocity space Vh and the pressure space Qh on triangles or tetrahedrons do not satisfy the inf-sup or Babuska–Brezzi condition: inf sup

q ∈Q h v ∈V h

∫ q∇⋅ vdV

Ω

∫ q dV ∫ ∇v 2

Ω

2

dV

≥β>0

(2.65)

Ω

(they are unstable), whereas continuous, piecewise quadratic velocities and continuous, piecewise linear pressures are inf-sup stable. A popular inf-sup stable element pair on quadrilaterals consists of continuous, piecewise biquadratic velocities and discontinuous, piecewise linear pressures (see Figure 2.3). It can be directly extended to the 3-D case. Summarizing the aspect of inf-sup stable ﬁnite element approximations we ﬁnd that a large number of pairs are known leading to optimal error estimates (Girault and Raviart, 1986; Brezzi and Fortin, 1991; Matthies and Tobiska, 2002, Matthies and Tobiska, 2005). Moreover, since the mid 1980s the technique of adding 1) Inf-sup stable ﬁnite element pairs satisfy the Babuska–Brezzi condition.

2.6 Implementation in FLUENT, MooNMD, COMSOL and ProMoT

weighted residuals of the differential equation has been also used to circumvent the inf-sup condition and to allow equal order interpolations for velocity and pressure. It is called the pressure-stabilized Petrov–Galerkin (PSPG) approach. Note that the combined SUPG/PSPG method is widely used in the CFD community due to its ability to handle instabilities caused by dominated convection and violating the inf-sup condition. The LPS method is even more attractive since the same stabilizing effect can be attained with less computational effort and by adding symmetric stabilizing terms. Let us ﬁnally mention that each discretization method (FDM, FVM, FEM) leads to a large system of algebraic equations, the solution of which requires powerful computers. In particular for complex three-dimensional problems and higher order discretizations one quickly reaches the limit of memory and processor speed. Therefore, efﬁcient methods for solving the large systems of algebraic equations are also needed. Fast iterative methods are preferable since they do not allocate additional memory during the solution process. Note that the discretization of the incompressible Navier–Stokes equations leads to a coupled system for velocity and pressure unknowns for which special iterative methods have been developed. The semi-implicit method for pressure-linked equation (SIMPLE) and its variants are popular in ﬁnite volume discretizations (Noll, 1993; Ferziger and Peric, 1996). For ﬁnite element discretizations multi-level methods with a multiplicative Vanka type smoother belong to the fastest methods. They are based on a block Gauss–Seidel type smoother and use a hierarchy of grid levels. An advanced multi-level multidiscretization solver which combines the advantage of high accuracy of higherorder ﬁnite element discretizations with the computational efﬁciency of multi-grid methods for low-order ﬁnite elements has been developed and numerically tested by (John et al., 2002).

2.6 Implementation in FLUENT, MooNMD, COMSOL and ProMoT

Powerful tools of process simulation and analysis, modern mathematical methods and efﬁcient algorithms are essential for the successful treatment of membrane reactors. In the present work, simulations based on CFD have been performed by FLUENT, MooNMD and COMSOL Multiphysics (COMSOL, 2006). The inhouse FEM software package MooNMD (John and Matthies, 2004) turned out to have advantages in case of special ﬂuid–dynamic investigations due to the accessibility of its source code. For solving reduced 1-D + 1-D models toolbox software packages such as ProMoT/Diva and MATLAB have been applied. The use of FLUENT, MooNMD and ProMoT is discussed in the following sections. 2.6.1 Application of FLUENT

The solution of the partial differential equations in FLUENT is based on the control–volume technique. FLUENT 6.2 allows to choose either of two numerical

49

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2 Modeling of Membrane Reactors

solvers: segregated or coupled solver (Fluent, 2006). The two numerical methods employ a similar discretization process, but the approach used to linearize and solve the discretized equations is different (Fluent, 2006). For the simulations the segregated solver was used, by which the governing equations are solved sequentially. At ﬁrst, ﬂuid properties are updated, based on the current solution. Each of the momentum equations is solved using the current values for pressure and face mass ﬂuxes, in order to update the velocity ﬁelds. If obtained velocities do not satisfy the continuity equation, the pressure correction equation is then solved to obtain the necessary corrections to the pressure and velocity ﬁelds and the face mass ﬂuxes. In consequence, the balances for the scalars are solved with the updated values for velocities and pressure. These steps are continued until the convergence criteria are fulﬁlled (Fluent, 2006). Referring to the simulation parameters, the ﬁrst-order upwind discretization was chosen for the convective ﬂuxes. For the approximation of the pressure gradients from the control volume center to the volume faces, the standard pressure interpolation scheme was used, taking into account the momentum equation coefﬁcients. The pressure–velocity coupling was achieved by using the SIMPLE algorithm. The total and component mass balances and energy balance were controlled for the whole computational domain for each simulation and on the basis of the conservative character of the control–volume method always fulﬁlled. The source terms in the momentum and mass balances and the material properties of gases and porous media were deﬁned for the different reactor zones in separate equations using user-deﬁned functions (UDF). 2.6.2 Application of MooNMD

The C++ ﬁnite element package MooNMD (John and Matthies, 2004) was developed at the Institute of Analysis and Numerics at the University of Magdeburg as a result of Mathematics and object-oriented Numerics in MagDeburg. It is based on the discretization of partial differential equations by mapped ﬁnite elements. In contrast to most commercial software products the MooNMD code is open and fully extendable. This allows one to study the properties of advanced numerical schemes and to implement newly developed concepts for the robust and efﬁcient solution of the nonlinear algebraic systems of equations. The package is in particular suited for the solution of incompressible ﬂow problems in two- and threedimensional domains decomposed into triangular/tetrahedral and quadrilateral/ hexahedral meshes, respectively. Several benchmark computations have been performed using MooNMD which show its high accuracy and wide range of applicability (John, 2002; Lavrova et al., 2002; Ganesan and Tobiska, 2008; Iliescu et al., 2003). The most important features of MooNMD are:

•

Higher-order ﬁnite elements of conforming and non-conforming type based on the concept of a family of reference mappings (Matthies and Tobiska, 2002, 2005)

2.6 Implementation in FLUENT, MooNMD, COMSOL and ProMoT

•

Isoparametric ﬁnite elements for better approximation of domains with curved boundaries

•

Stabilization techniques like SUPG (Matthies and Tobiska, 2001; John et al., 1998) or LPS (Matthies, Skrzypacz, and Tobiska, 2007, 2008) to handle instabilities caused by dominated convection and/or unstable ﬁnite element pairs

•

Various shock capturing methods to suppress spurious oscillations (John and Knobloch, 2007, 2008)

•

Postprocessing tools to enhance accuracy by superconvergence (Matthies, Skrzypacz, and Tobiska, 2005)

•

State-of-the-art iterative solvers like ﬂexible GMRES (Saad 2003), multiplediscretization multi-level approach with Vanka type smoothers for mixed problems (John et al., 2002) and fast direct solver UMFPACK (Davis, 2004)

•

Built-in output to graphical tools, for example, VTK (Schröder, Martin, and Lorensen, 2006)

The ﬂexibility and adaptivity of MooNMD to user-deﬁned problems allow full control over the design of decoupling strategies and the solution process for systems of nonlinear partial differential equations. 2.6.3 Application of ProMoT

Both FLUENT and MoonMD are simulation tools in the sense that they expect a fully developed model equation system from the user and provide an efﬁcient numerical solution of this system. The approach of the process modeling tool ProMoT (Tränkle et al., 2000) presented in this subsection is different: instead of solving a given model, ProMoT aims at supporting the model development process. The numerical solution of the models generated by ProMoT is done in other tools like DIVA (Köhler et al., 2001), MATLAB, or DIANA (Krasnyk et al., 2006). The need for computer-aided modeling of membrane reactors results from the complexity of the model approaches described above. A membrane reactor model has to meet demands on validity of the model on the one hand, but also on implementation issues on the other hand. Meeting the ﬁrst demand, that is, developing a realistic membrane reactor model, is an iterative process: a model typically requires a lot of reﬁnement until it proves to be adequate for the solution of a given problem. Once a model has been validated and found to be applicable to a design or a control problem, the right way to implement the model becomes important. Traditionally, the model of a chemical apparatus is implemented in a monolithic way without much internal structuring. This makes the understanding and debugging of the model difﬁcult. Monolithically structured models are not very transparent and are hardly reusable for another modeler. Furthermore, the implementation of complicated differential equations in a ﬂow-sheet simulator is

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2 Modeling of Membrane Reactors

tedious and error prone. Finally, in most simulation tools it is the responsibility of the modeler to formulate his models in a manner suitable for numerical treatment, for example, to avoid a higher differential index of a differential algebraic system. From the requirements on model formulation and on model implementation, the main objectives of a computer-aided modeling tool follow immediately: a modeling tool should: (a) let a user concentrate on the physical modeling task and relieve him from mechanical coding work, (b) increase the reusability and transparency of existing models, (c) simplify the debugging process during model development and (d) provide libraries of predeﬁned building blocks for standard modeling tasks such as reaction kinetics, physical properties, or transport phenomena. The process modeling tool ProMoT is a software environment that possesses all the properties listed above. It is used as a framework for a model library of structured membrane reactor models. The development of such a library consists of two main steps: (a) the choice of a suitable structuring methodology for the models and (b) the implementation of the structured models in ProMoT. Both steps are discussed in the following. The usefulness of a model library strongly depends on the structure of the implemented models. Typically, process models in ﬂow-sheet simulators are formulated in terms of process unit models. However, process unit models are not suitable elementary units of a model library, because they are too complex and contain too much information on a speciﬁc process. In view of the many existing variants of chemical reactors, a library of reactor models will always be incomplete. It seems more promising to divide the process unit models further into smaller subunits and to store the subunits in the model library. The network theory of chemical processes (Gilles, 1998; Mangold, Motz, and Gilles, 2002) gives a guideline for the internal structuring of process unit models. The basic idea is to describe a process model by two types of elementary functional units: components and coupling elements. Components possess a hold-up for physical quantities like energy, mass, or momentum. They are described by a thermodynamic state or a state vector. The state of a component may be changed by ﬂuxes or ﬂux vectors. The task of the second class of functional units, the coupling elements, is to determine these ﬂux vectors. In accordance with the principles of irreversible thermodynamics, it is assumed that the ﬂux vector is an algebraic function of potential differences and potential gradients. As an example, consider the general balance (same as Equation 2.5): ∂ ( ρϕ ) = −∇⋅ ( ρϕ v ) − ∇jϕ + sϕ ∂t

(2.66)

In the methodology of the network theory, the left-hand side of the above equation can be seen as a storage for ﬁeld quantity ρϕ, and the three terms on the righthand side can be represented by coupling elements for convective transport, nonconvective transport and internal sinks and sources, respectively. Figure 2.4 shows a formal graphical representation of Equation 2.66, which uses the symbols introduced in (Gilles, 1998).

2.6 Implementation in FLUENT, MooNMD, COMSOL and ProMoT

+

+

+

Δ

–

· (rjv)

Δ

rj

+

– jj

s·j

Figure 2.4 Graphical representation of the general balance by the symbols of the network theory (Gilles, 1998).

The storage element ρϕ delivers information on its internal state to the three coupling elements, which in turn use this information to determine the ﬂuxes that change the component’s state. One should note that Figure 2.4 is simpliﬁed, because in general it is not only the ﬁeld quantity ϕ but the complete thermodynamic state vectors that determine the ﬂuxes. The decomposition of a process model into components and coupling elements can be carried out on different hierarchical levels. A connected system of components and coupling units on one level can always be considered as an aggregated component on the next higher level. For example, models of process units can be considered as components of a plant model. This structures the plant on the level of process units. However, the model of a process unit can be decomposed into models of thermodynamic phases interacting via phase boundaries. Therefore, thermodynamic phases can be considered as components on a level of phases; the phase boundaries are the corresponding coupling elements. Finally, a thermodynamic phase is able to store macroscopic thermodynamic quantities like mass or internal energy, the components on the level of macroscopic thermodynamic storages. The coupling elements on that level are mass and energy transport phenomena inside a phase as well as chemical reactions. The decomposition of the general balance (2.66) shown in Figure 2.4 occurs on the level of storages. By applying the described structuring concept, a model library of distributed dynamic packed-bed and membrane reactor models has been implemented in the process modeling tool ProMoT. The model library was described in detail in (Mangold, Ginkel, and Gilles, 2004). Only a brief overview is given here. The library contains modules for the formulation of models for heterogeneous catalytic reactors with gas phase reactions. Dynamic homogeneous, heterogeneous and pseudo-homogeneous models with one space coordinate are considered. The model library in ProMoT differs from a library of process units in a traditional ﬂow-sheet simulator mainly in two respects. The ﬁrst difference is the deep structuring below the level of process units. A membrane reactor model is decomposed into models of several thermodynamic phases, for example, for the membrane, the sweep gas side and the tubular side. Each phase model is built up from

53

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modules for mass storage and energy storage, from modules for transport phenomena inside a thermodynamic phase like convection, diffusion, or heat conduction, as well as from modules describing sinks and sources in the phase due to chemical reaction. These modules on the level of storages are the elementary modeling entities in the model library. The advantage of this ﬁne granulation of the model structure is that a comparatively small amount of elementary modeling units or building blocks sufﬁces to describe a wide variety of membrane reactor models. The second difference is that object oriented concepts like aggregation and inheritance can be used to formulate a model. Aggregation can be seen as the software representation of the decomposition levels described above. Inheritance stands for the ability of a model to adopt properties like equations or variable deﬁnitions from another model, the so-called super-class. In ProMoT it is possible to use multiple inheritance, that is, a model can inherit from several super-classes. In the following, the simulation of a composite membrane as described by (Hussain, 2006) is discussed. The membrane consists of four layers of varying thickness and porosity. A model of the membrane in a testing environment as shown in Figure 2.5 is to be developed in ProMoT. In a ﬁrst step, a model of a single membrane layer is constructed from predeﬁned building blocks in the model library. The isothermal dusty gas model is used to describe the membrane layer. A screenshot of the single layer model in ProMoT is shown in Figure 2.6. It can be seen that the model contains two spatially distributed storage elements for total mass and component masses corresponding to total mass and component mass balances. As the membrane is assumed to be isothermal, a reservoir with constant temperature is added instead of an energy storage. A connecting element,

Figure 2.5 Scheme of a testing environment for a composite membrane with four layers denoted as (1)–(4).

2.6 Implementation in FLUENT, MooNMD, COMSOL and ProMoT

Figure 2.6

Structured ProMoT model of a single layer of the composite membrane.

which contains phenomenological relations of the mass ﬂuxes according to the dusty gas model, describes the mass transport through the membrane. Two additional building blocks, one of them converting partial densities into mass fractions and the other computing the total pressure from the ideal gas law, complete the model. Extensions of the single layer model are straightforward, for example, the extension to a nonisothermal model by substituting the constant temperature reservoir with an energy storage, or the extension to a reactive membrane layer by adding a reactive connecting element. Using aggregation, the assembly of connected modules in Figure 2.6 can be fused to a new modeling entity, which describes a single membrane layer. In order to model the composite membrane in Figure 2.5, four of those aggregated modules are necessary. Each of the four modules possesses identical model equations, but a different set of model parameter values to account for the different properties of the four membrane layers.

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Figure 2.7 Structured ProMoT model of the membrane process shown in Figure 2.5. The single layer models can be decomposed into the structure shown in Figure 2.6.

The ProMoT model of the complete membrane is shown in Figure 2.7. In addition to the building blocks for the membrane layers it contains connecting elements for the internal boundary conditions between the layers and modules for the description of the gas bulks on the left-hand side and on the right-hand side of the membrane.

2.7 Conclusion

The diversity concerning conﬁguration and operation of membrane reactors requires a general, common frame for developing and solving respective models. After presenting this frame, we can proceed in the following chapters with the identiﬁcation of model parameters and the detailed treatment of speciﬁc membrane reactor conﬁgurations. Hereby, selected parts of the theoretical models introduced and the tools described are used.

Notation used in this Chapter Latin Notation

A B0 C

m2 m2 m2/s

cp c Dij d e

J/(kg K) mol/m3 m2/s m J/kg

area permeability parameter diffusion coefﬁcient matrix in DGM speciﬁc heat capacity molar concentration diffusion coefﬁcient diameter speciﬁc energy

Notation used in this Chapter

F F 0 f f1 f2 g h h h 0 hi* I K0 l L M M m n˙ n p q R Ri rj r s T t u ui V v vf v vi* y y z

Pa/m N/m3 Pa s/m2 Pa s2/m3 m/s2 J/kg J/mol J/mol J/mol m m m kg kg/kmol kg/(m2 s) md/s mol/(m2 s) Pa W/m2 J/(mol K) kg/(m3 s) mol/(kg s) m mol/(m2 s), kg/(m3 s) K, °C s m/s m/s m3 m/s m/s m3/mol m3/mol

m

driving force vector in DGM diffusion parameter force source term viscous resistance factor inertial resistance factor gravitational acceleration speciﬁc enthalpy molar enthalpy molar enthalpy of formation partial molar enthalpy identity matrix knudsen parameter mean free path length mass molar mass mass ﬂux permeate ﬂux of the membrane molar ﬂux pressure heat ﬂux universal gas constant reaction source term rate of reaction radial coordinate source term temperature time volume average velocity velocity of component i volume mass average velocity, superﬁcial velocity interstitial velocity molar volume partial molar volume of component i mass fraction mole fraction axial coordinate

Greek Notation

α Γ

molar ﬂux ratio parameter matrix of non-ideal coefﬁcients

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2 Modeling of Membrane Reactors

ε η κ λ μ νij ρ ρi* ρf τ

τ ϕ

Pa s Pa s W/(m K) J/mol kg/m3 kg/m3 kg/m3 Pa

porosity dynamic viscosity dilatational viscosity thermal conductivity chemical potential stoichiometric coefﬁcient density partial density of component i average density tortuosity stress tensor arbitrary ﬁeld quantity

Super- and Subscripts

b cat cor D Diff e, eff f g i i,j K M m mol n nr o p p pb pore r ref s SS T

boundary catalyst corrected, correction total diffusion molecular diffusion effective ﬂuid gas inner (tube side) component index, reaction index Knudsen Stefan–Maxwell membrane molecule number of components, inert species number of reactions outer (shell side) at constant pressure particle pseudo-binary pore radial reference solid shell side at constant temperature

References

TS t v x y z ϕ ϕ 0 ∞ *

tube side transposed viscous ﬂow in x-direction in y-direction axial for arbitrary ﬁeld quantity in ϕ-direction (circumferential) initial value in the core of the bed partial

References Amann, H. (2001) On the strong solvability of the Navier-Stokes equations. J. Math. Fluid Mech., 2, 16–98. Baranowski, B. (1975) NichtgleichgewichtsThermodynamik in der physika-lischen Chemie, Dt. Verl. für Grundstofﬁndustrie, Leipzig. Bird, R.B., Stewart, W.E., and Lightfoot, E.N. (2002) Transport Phenomena, John Wiley & Sons, Inc., New York. Bosanquet, C.H. (1944) British TA Rept., BR-507:770. Brezzi, F., and Fortin, M. (1991) Mixed and Hybrid Finite Element Methods, Springer, Berlin. Brooks, A.N., and Hughes, T.J.R. (1982) Streamline upwind/Petrov-Galerkin formulation for convection dominated ﬂows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg., 32, 199–259. Chou, S.H., and Ye, X. (2007) Uniﬁed analysis of ﬁnite volume methods for second order elliptic problems. SIAM J. Numer. Anal., 45 (4), 1639–1653. COMSOL (2006) Handbook, COMSOL Multiphysics 3.2, 1997–2007 COMSOL, Inc., All Rights Reserved. Cussler, L. (1997) Diffusion, Mass Transfer in Fluid Systems, Cambridge University Press. Davis, T.A. (2004) Algorithm 832: UMFPACK V4.3 – an unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw., 30 (2), 196–199.

de Groot, S.R., and Mazur, P. (1984) Non-Equilibrium Thermodynamics, Dover Publ., New York. Deriagin, B.V., and Bakanov, S.P. (1957) Theory of gas ﬂow in a porous body near the Knudsen region: pseudomolecular ﬂow. Sov Phys. Dokl., 2, 326. Dixon, A., and Nijemeisland, M. (2001) CFD as a design tool for ﬁxed-bed reactors. Ind. Eng. Chem. Res., 40, 5246–5254. Dixon, A., Nijemeisland, M., and Stitt, H. (2003) CFD simulation of reaction and heat transfer near the wall of a ﬁxed bed. Int. J. Chem. React. Eng., 1, A22. Eckhaus, W. (1973) Matched Asymptotic Expansions and Singular Perturbations, Mathematic Studies 6, North Holland/ American Elsevier, Amsterdam, New York. Elnashaie, S.S.E.H., and Elshishini, S. (1993) Modelling, Simulation and Optimization of Industrial Fixed Bed Catalytic Reactors, Gordon and Breach, London. Ergun, S. (1952) Fluid ﬂow through packed columns. Chem. Eng. Prog., 48, 9–94. Evans, R., Watson, G., and Maso, E. (1962) Gaseous diffusion in porous media at uniform pressure. J. Chem. Phys., 35, 2076–2083. Ferziger, J.H., and Peric, M. (1996) Computational Methods for Fluid Dynamics, Springer, Berlin. FLUENT (2006) FLUENT 6.2 Help. Forchheimer, P. (1901) Wasserbewegung durch Goden. Zeits. V. deutsch. Ing., 45, 1782–1788.

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2 Modeling of Membrane Reactors Fuller, E., Schettler, P., and Giddings, J. (1966) New method for prediction of binary gas-phase diffusion coefﬁcients. Ind. Eng. Chem. Res., 58, 18–27. Galdi, G.P. (1994) An Introduction to the Mathematical Theory of the Navier-Stokes Equations,Vol. I, Linearized Steady Problems, Vol. II, Nonlinear Steady Problems, Springer, New York. Ganesan, S., and Tobiska, L. (2008) An accurate ﬁnite element scheme with moving meshes for computing 3D-axisymmetric interface ﬂows. Int. J. Numer. Methods Fluids, 57 (2), 119–138. Ganesan, S., Matthies, G., and Tobiska, L. (2008) Local projection stabilization of equal order interpolation applied to the Stokes problem, Math. Comp., electr. published May 9, 2008. Georgieva, K., Mednev, I., Handtke, D., and Schmidt, J. (2005) Inﬂence of the operating conditions on yield and selectivity for partial oxidation of ethane in a catalytic membrane reactor. Catal. Today, 101, 168–176. Gilles, E.D. (1998) Network theory for chemical processes. Chem. Engng. Technol., 21, 121–132. Girault, V., and Raviart, P.-A. (1986) Finite Element Methods for Navier-Stokes Equations, Springer, Berlin. Haase, R. (1963) Thermodynamik Der Irreversiblen Prozesse, Steinkopff, Darmstadt. Hunt, M., and Tien, C. (1990) Non-Darcian ﬂow, heat and mass transfer in catalytic packed-bed reactors. Chem. Eng. Sci., 45 (1), 55–63. Hussain, A. (2006) Heat and mass transfer in tubular inorganic membranes, PhD thesis, Otto-von-Guericke-Universität, Magdeburg. Iliescu, T., John, V., Layton, W., Matthies, G., and Tobiska, L. (2003) A numerical study of a class of LES models. Int. J. Comput. Fluid Dynamics, 17 (1), 75–85. Jackson, R. (1977) Transport in Porous Catalysts, Elsevier, Amsterdam. John, V. (2002) Higher order ﬁnite element methods and multigrid solvers in a benchmark problem for the 3D NavierStokes equations. Int. J. Numer. Methods Fluids, 40 (6), 775–798.

John, V., and Knobloch, P. (2007) On spurious oscillations at layer diminishing (SOLD) methods for convection-diffusion equations, Part I – a review. Comput. Methods Appl. Mech. Engrg, 196, 2197–2215. John, V., and Knobloch, P. (2008) On spurious oscillations at layer diminishing (SOLD) methods for convection-diffusion equations, Part II – Analysis for P1 and Q1 ﬁnite elements. Comput. Methods Appl. Mech. Engrg, 197, 1997–2014. John, V., and Matthies, G. (2004) MooNMD – a program package based on mapped ﬁnite element methods. Comput. Vis. Sci., 6 (2–3), 163–169. John, V., Matthies, G., Schieweck, F., and Tobiska, L. (1998) A streamline-diffusion method for nonconforming ﬁnite element approximations applied to convectiondiffusion problems. Comput. Methods Appl. Mech. Engrg, 166 (1–2), 85–97. John, V., Knobloch, P., Matthies, G., and Tobiska, L. (2002) Non-nested multi-level solvers for ﬁnite element discretizations of mixed problems. Computing, 68, 313–341. Kerkhof, P., and Geboers, M. (2005) Towards a uniﬁed theory of isotropic molecular transport phenomena. AIChE J., 51 (1), 79–121. Knobloch, P., and Tobiska, L. (2008) On the Stability of the Finite Element Discretization of Convection-Diffusion-Reaction Equations, Preprint 08-11, Otto-von-GuerickeUniversity Magdeburg. Köhler, R., Mohl, K.D., Schramm, H., Zeitz, M., Kienle, A., Mangold, M., Stein, E., and Gilles, E.D. (2001) Method of lines within the simulation environment DIVA for chemical processes, in Adaptive Method of Lines (eds A. van de Wouver, P. Saucez, and W.E. Schiesser), Chapman & Hall, London, pp. 371–406. Kracmar, S., and Nestupa, J. (2001) A weak solvability of a steady variational inequality of the Navier-Stokes type with mixed boundary conditions. Nonlinear Anal., 47, 4169–4180. Krasnyk, M., Bondareva, K., Milokhov, O., Teplinskiy, K., Ginkel, M., and Kienle, A. (2006) The ProMoT/DIANA simulation environment, in Proceedings of the 16th European Symposium on Computer Aided

References Process Engineering (eds W. Marquardt and C. Pantelides), Elsevier, London, pp. 445–450. Krishna, R., and van Baten, J.M. (2009) An investigation of the characteristics of Maxwell-Stefan diffusivities of binary mixtures in silica nanopores. Chem. Eng. Sci., 64, 870–882. Lavrova, O., Matthies, G., Mitkova, T., Polevikov, V., and Tobiska, L. (2002) Finite element methods for coupled problems in ferrohydrodynamics, in Challanges in Scientiﬁc Computing–CISC (ed. E. Bänsch), Springer, pp. 160–183, Lect. Notes Comput. Sci. Eng. 35, 2003. Lions, P.-L. (1996) Mathematical Topics in Fluid Mechanics, Vol. 1 Incompressible Models, Vol. 2 Compressible Models, Oxford Science Publications. Lucas, K., and Luckas, M. (2002) Berechnungsmethoden Für Stoffeigenschaften, Section Da in: VDI-Wärmeatlas, 9th edn, Springer, Berlin. Mackey, M.C. (1971) Kinetic theory model for ion movement through biological membranes. Biophys. J., 11, 75–90. Mangold, M., Motz, S., and Gilles, E.D. (2002) Network theory for the structured modelling of chemical processes. Chem. Engng. Sci., 57, 4099–4116. Mangold, M., Ginkel, M., and Gilles, E.D. (2004) A model library for membrane reactors implemented in the process modeling tool ProMoT. Comput. Chem. Eng., 28, 319–332. Manjhi, N., Verma, N., Salem, K., and Mewes, D. (2006) Lattice Boltzmann modelling of unsteady-state 2D concentration proﬁles in adsorption bed. Chem. Eng., Sci., 61, 2510–2521. Masel, R. (2001) Chemical Kinetics and Catalysis, John Wiley & Sons, Inc., New York. Mason, E.A., Malinauskas, A.P., and Evans, R.B. (1967) Flow and diffusion of gases in porous media. J. Chem. Phys., 46, 3199–3216. Matthies, G., Skrzypacz, P., and Tobiska, L. (2005) Superconvergence of a 3D ﬁnite element method for stationary Stokes and Navier-Stokes problems. Numer. Methods Part. Diff. Equat., 21, 701–725. Matthies, G., Skrzypacz, P., and Tobiska, L. (2007) A uniﬁed convergence analysis

for local projection stabilization applied to the Oseen problem. ESAIM: M2AN, 41 (4), 713–742. Matthies, G., Skrzypacz, P., and Tobiska, L. (2008) Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions. ETNA, 32, 90–105. Matthies, G., and Tobiska, L. (2001) The streamline-diffusion method for conforming and nonconforming ﬁnite elements of lowest order applied to convection-diffusion problems. Computing, 66 (4), 343–364. Matthies, G., and Tobiska, L. (2002) The inf-sup condition for the mapped Q_k-P_k-1∧disc element in arbitrary space dimensions. Computing, 69, 119–139. Matthies, G., and Tobiska, L. (2005) Inf-sup stable nonconforming ﬁnite elements of arbitrary order on triangles. Numer. Math., 102, 293–309. Matthies, G., and Tobiska, L. (2007) Mass conservation of ﬁnite element methods for coupled ﬂow-transport problems. Int. J. Comput. Sci. Math., 1, 293–307. Melin, T., and Rautenbach, R. (2007) Membranverfahren: Grundlagen der Modul- und Anlagenauslegung, Springler, Berlin. Noll, B. (1993) Numerische Strömungsmechanik, Springer, Berlin. Poling, B.E., Prausnitz, J.M., and O’Connell, J.P. (2001) The Properties of Gases and Liquids, McGraw-Hill, New York. Reid, R.C., Prausnitz, J.M., and Sherwood, T.K. (1977) The Properties of Gases and Liquids, 3th edn, McGraw-Hill, New York. Russo, R., and Simader, C. (2006) A note on the existence of solutions to the Oseen system in Lipschitz domains. J. Math. Fluid Mech., 8 (1), 64–76. Saad, Y. (2003) Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia. Sani, R.L., and Gresho, P.M. (1994) Resume and remarks on the open boundary condition minisymposium. Int. J. Numer. Methods Fluids, 18, 983–1008. Schröder, W., Martin, K., and Lorensen, B. (2006) The Visualization Toolkit: An Object-Oriented Approach to 3D Graphics, Kitware.

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2 Modeling of Membrane Reactors Tabata, M. (1977) A ﬁnite element approximation corresponding the upwind differencing. Mem. Numer. Math., 1, 47–63. Taylor, R., and Krishna, R. (1994) Multicomponent Mass Transfer, John Wiley & Sons, Inc., New York. Tota, A., Hlushkou, D., Tsotsas, E., and Seidel-Morgenstern, A. (2007) Packed bed membrane reactors, Chapter 5, in Modeling of Process Intensiﬁcation (ed. F.J. Keil), WileyVCH Verlag GmbH, Weinheim, pp. 99–148. Tränkle, F., Zeitz, M., Ginkel, M., and Gilles, E.D. (2000) ProMoT: a modeling tool for chemical processes. Math. Comp. Model. Dyn. Syst., 6, 283–307. Tsotsas, E. (1991) Über Die Wärme- Und Stoffübertragung in Durchströmten

Festbetten: Experimente, Modelle, Theorien, VDI Fortschr, Ber., Ser. 3, No. 223, VDI Verlag, Düsseldorf. Varma, A., and Morbidelli, M. (1997) Mathematical Methods in Chemical Engineering, Oxford University Press. Wesselingh, J.A., and Krishna, R. (2000) Mass Transfer in Multi-Component Mixtures, Delft University Press. Young, J.B., and Todd, B. (2005) Modelling of multi-component gas ﬂows in capillaries and porous solids. Int. J. Heat Mass Transf., 48, 5338–5353. Zajaczkowski, W.M. (2007) Some global regular solutions to Navier-Stokes equations, Math. Methods Appl. Sci., 30 (2), 123–151.

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3 Catalysis and Reaction Kinetics of a Model Reaction Frank Klose, Milind Joshi, Tanya Wolff, Henning Haida, Andreas Seidel-Morgenstern, Yuri Suchorski, and Helmut Weiß 3.1 Introduction

The development of new and the improvement of existing reactor concepts is difﬁcult without understanding the reaction mechanism and – if a catalyst is used – its operation principles. In the ideal case an accurate kinetic model with detailed structure–activity relations would be available. However, in industrial practice in general only simpliﬁed strategies are applied in order to minimize experimental effort and to reduce the complexity of the corresponding mathematical expressions. Often simpliﬁed kinetic models of the power law type are used to describe reaction rates and catalytic performance for a limited parameter range. Nevertheless, for the understanding and the correct prediction of the performance of alternative reactor concepts, as the membrane reactors treated in this book, a more detailed understanding of the kinetic relations is essential. In membrane reactors the concentration proﬁles of the reactants and the contact time proﬁles in the catalyst bed are inﬂuenced simultaneously. A reliable kinetic model has to describe also the reaction behavior for conditions which are far from those present in conventional packed-bed reactors. In order to deliver reliable data for the comparison between conventional and membrane reactors on the one hand, and between different membrane reactor concepts on the other, it is important to study the same reaction system and to apply the same catalyst. In this and the following chapters, the focus is set on the catalyzed oxidative dehydrogenation of ethane (ODHE). Although this reaction is currently far from a wide industrial application, it has several advantages for the purpose of this conceptual study:

•

The expected reaction network is limited to a rather low number of main products and byproducts, which facilitates mechanistic as well as kinetic studies.

•

There are no condensable products under reaction conditions, which is beneﬁcial for monitoring the reactor performance with high accuracy.

Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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3 Catalysis and Reaction Kinetics of a Model Reaction

•

The reactants and products can be efﬁciently and reliably studied by gas chromatography.

•

The reaction temperature is high enough to evaluate possible difﬁculties in the practical applications of the reactors, but also low enough to realize and to operate them safely on a pilot plant scale.

•

The performance of conventional packed-bed reactors is comparably poor, and positive effects of new reaction engineering strategies should be well detectable.

•

It should be possible to transfer major aspects of the ODHE to the selective oxidation of other hydrocarbons, for example, the oxidative dehydrogenation of propane (ODHP, see Chapter 5) or the selective oxidation of butane to maleic anhydride (Chapter 7).

Next to the choice of the reaction itself, the selection of a suitable catalyst is of importance. In particular, it should allow investigating the interplay between reactants, intermediates, products and the catalyst surface itself. With respect to the oxidative dehydrogenation of ethane, a wide variety of catalytic systems has already been studied and a considerable number of reviews published (Banares, 1999; Cavani and Triﬁro, 1999; Grasselli, 1999; Bhasin et al., 2001; Dai and Au, 2002). Based on the reaction mechanism, the catalytically active components can be divided into four main classes, namely: (a) reducible oxides of non-noble transition metals, including perovskites and related catalysts, (b) non-reducible oxides of the elements from the Ia, IIa and IIIb groups including lanthanoids, (c) platinumbased catalysts, usually applied for deep oxidation and (d) all catalysts not included in the previous classes. Beside from the reaction mechanism, these classes differ also in their operation temperatures and the maximum accessible ethylene yields. In a study of ODHE for different membrane reactors of the distributor type and a comparison with conventional reactors it is important to use the same active catalyst in all experiments. The goal of the work presented here was not to ﬁnd an optimized catalyst, but to use one which: (i) can be prepared in an easy and reproducible way and in larger quantities, (ii) is rather cheap in preparation and (iii) has proven before to be catalytically active in ODHE. All these prerequisites are fulﬁlled for some of the class (a) catalysts, that is, reducible oxides of non-noble transition metals. In particular, it is possible to produce catalytically active layers of these materials on different supports like, for example, alumina, silica or titania. For this study, supported vanadia catalysts were chosen for reasons which are explained in more detail below. This chapter is organized as follows. We start with a short description of the reaction network, which was deduced from results of experimental studies using vanadia catalysts. A preliminary power law analysis shows that a distributed-feed concept should have the potential to improve the selectivity towards the desired hydrocarbon, for example, ethylene. We then further describe the preparation, characterization and properties of the vanadia catalysts used. Finally, we provide results of a more detailed analysis and suggest a quantitative model for the reaction kinetics of the reaction network valid for the supported vanadium oxide catalyst.

3.2 The Reaction Network of the Oxidative Dehydrogenation of Ethane

3.2 The Reaction Network of the Oxidative Dehydrogenation of Ethane

Using the above mentioned vanadia catalysts supported on γ-alumina (VOx/γAl2O3) which are described in detail below, the reaction network of the oxidative dehydrogenation of ethane has been investigated in depth performing experiments in conventional packed-bed reactors. In these experiments, the feed concentrations of both hydrocarbon and oxygen, the temperature, the gas hourly space velocity (GHSV) and the vanadium loading on the catalyst support have been varied in a systematic manner. Here only essential ﬁndings of these investigations are given. The results of a more detailed kinetic analysis are described in Section 3.4. Summarizing the experimental ﬁndings, the following main reactions were identiﬁed (Klose et al., 2004): C2H6 + 0.5O2 → C2H4 + H2O

(3.1)

C2H6 + 3.5O2 → 2CO2 + 3H2O

(3.2)

C2H4 + 2O2 → 2CO + 2H2O

(3.3)

C2H4 + 3O2 → 2CO2 + 2H2O

(3.4)

CO + 0.5O2 → CO2

(3.5)

C2H6 + 2.5O2 → 2CO + 3H2O

(3.6)

Reaction 3.3 was formulated due to the fact that no acetaldehyde could be detected in the measurements reported below. In this reaction are lumped the acetaldehyde formation from ethylene, its oxidation to CO and the direct ethylene oxidation to CO: C2H4 + 0.5O2 → CH3CHO CH3CHO + 1.5O2 → 2CO + 2H2O C2H4 + 2O2 → 2CO + 2H2O

(3.7)

Under oxygen-free conditions, a number of side reactions contributing to ethylene formation and to its consumption have also to be taken into account. Such side reactions are: C2H6 + CO2 → C2H4 + CO + H2O C2H4 + 4CO2 → 6CO + 2H2O C2H4 → 2C + 2H2

(3.8)

2CO → C + CO2 A major challenge is the accurate measurement of the extent of these side reactions. Especially, the reliable quantiﬁcation of carbon deposits on the catalyst surface by ethylene pyrolysis and Boudouard reactions is very complicated.

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r1 C 2 H6

C 2 H4 r6

r3 CO r5

r2

r4

CO2 Figure 3.1 The proposed reaction network for the oxidative dehydrogenation of ethane (ODHE) over VOx/Al2O3 catalysts. The formation of carbon monoxide from ethane (r6) was neglected in the kinetic modeling. Table 3.1 Reaction rate orders of Reactions 3.1 to 3.5 with respect to C2H6, C2H4 and CO (α j)

and oxygen (βj) (Equation 3.9, Tóta et al., 2004), VOx-Cat.

αj βj

r1

r2

r3

r4

r5

0.88 0.02

0.75 0.24

0.84 0.11

0.87 0.20

1.13 0.13

Already in the ﬁrst experimental investigations using the laboratory reactor described later, it was found that Reaction 3.6 was not signiﬁcant and could be neglected. Thus, the ﬁve reactions shown in Figure 3.1 represent the reaction network considered below. The most important question regarding a successful membrane reactor concept is: can a distributed feed of one of the reactants improve the reactor performance? To answer this question simpliﬁed power law kinetics (Levenspiel, 1999) were assumed and the orders were estimated in a ﬁrst analysis of the experimental data described later. Hereby, the rate laws assumed were: α

β

j r j = k j cHC/CO cO2j

j = 1 ... 5

(3.9)

The results obtained revealed that the order of the reaction of ethane to ethylene (3.1) with respect to oxygen, β1, is approximately zero, while this order is higher for the other four steps (β2 … β5; Table 3.1; Tóta et al., 2004). Referring to Section 1.6, it can be stated that the prerequisite for a successful operation of a membrane reactor distributing oxygen is fulﬁlled.

3.3 Catalysts and Structure–Activity Relations

Due to the necessity to ﬁnd a catalyst well suited for the study of the membrane reactor concept, several non-noble transition metal oxides have been tested.

3.3 Catalysts and Structure–Activity Relations 100

67

100 Al2O3 1.4 % V/Al2O3 1.4 % Cr/Al2O3 1.3 % Fe/Al2O3 80

Ethylene selectivity / %

Ethane conversion / %

80

60

40

20

60

40

20

0

0 0

0.5

1

1.5

2 2.5 3 ~ ~ cO ,0/c C2H6,0 2

3.5

4

Figure 3.2 Ethane conversion (left) and selectivity towards ethylene (right) as a function of the oxygen to hydrocarbon ratio in the reactor feed for different catalytically active species. The most active species was

4.5

5

0

0.5

1

1.5

2 2.5 3 ~ ~ cO ,0/c C2H6,0 2

chromium (Δ), but the best tradeoff between activity and selectivity was achieved with the vanadium doped catalyst (䉫). The experimental conditions were MCat/V˙ = 558 kg s/m3, T = 863 K, Mcat = 3.1 g.

Figure 3.2 shows measured activities of vanadium, iron and chromium oxides on γ-Al2O3 as well as those of the bare γ-alumina support in the oxidation of ethane and the corresponding selectivity towards the desired product ethylene. As can be seen, CrOx and FeOx are both characterized by high conversion rates, but only low selectivities. In contrast, the conversion of ethane above VOx spread over γ-Al2O3 is rather low, but has the highest selectivity towards ethylene. It should be noted that the pure support material has a comparable activity but a selectivity of 100% towards the thermodynamically stable ﬁnal product CO2. Evaluating these ﬁndings vanadia-based catalysts on a γ-Al2O3 support were used in all subsequent studies. The following brieﬂy summarizes the state of knowledge on vanadia catalysts in the oxidative dehydrogenation of ethane. ODHE over vanadia catalysts belongs to the class of redox catalysis reactions following the Mars–van Krevelen mechanism (Mars and van Krevelen, 1954), which is found also in the oxidation of higher hydrocarbons (Busca, 1996; Magagula and van Steen, 1999). In the ﬁrst step of this mechanism, the hydrocarbon is oxidized by the catalyst, which itself is reduced

3.5

4

4.5

5

68

3 Catalysis and Reaction Kinetics of a Model Reaction

and in a second step re-oxidized by an oxidant from the surrounding gas phase, for example, O2 or CO2. In general, a reaction network consisting of: (a) the selective oxidation yielding oleﬁns or oxygenates, (b) the parallel “deep oxidation” of the primary hydrocarbon to COx and (c) the consecutive oxidation of the oleﬁns or oxygenates to COx is to be expected. Thus, selective oxidation is a kinetically controlled reaction. It is evident that the formation of carbon oxides is not desired as it minimizes selectivity and yields of the oxidation products of interest, in this case ethylene. The pure vanadium oxide (V2O5) is known to be rather inactive (Oyama and Somorjai, 1990; Le Bars et al., 1992) and has also unfavorable mechanical properties when stable pellets or monoliths are needed (Chary et al., 2003; Reddy and Varma, 2004). For these reasons, vanadia is typically deposited onto high-surfacearea supports like γ-alumina, silica, zeolites, titania or zirconia. Usually, the support is loaded with a suitable vanadium compound (precursor), for example, by impregnation, grafting or chemical vapor deposition (CVD) techniques and afterwards treated at elevated temperatures under an oxidizing environment. During this calcination step, the vanadium precursor converts to the oxide, which undergoes a chemical interaction with the support yielding the formation of M-O–V bonds (M = metal cation of the support material). At low and moderate loadings, this results in the formation of a two-dimensional vanadate “monolayer” with a high dispersion of V species. Only if the surface is overloaded the excess vanadia agglomerates and forms three-dimensional V2O5 crystallites (Blasco and López Nieto, 1997; Mamedow and Cortés Corberán, 1995; Banares, 1999). The monolayer capacity for vanadia and the strength of the support–vanadia interaction depend on the type of the support material. The nature of the vanadia species formed on different support materials is already the subject of several reviews (e.g., Weckhuysen and Keller, 2003; Haber, Witko, and Tokarz, 1999; Deo, Wachs, and Haber, 1994; Grzybowska-Swierkosz, 1999). The most prominent concept postulates the existence of monovanadates and divanadates, polyvanadates and bulk-like V2O5 structures. Monovanadates (VO43−) as the most dispersed vanadia species should appear predominantly at low V loadings, where the tetrahedral VO4 base unit is assumed to consist of one V=O double bond and three M-O–V bonds to the support. With moderately increased V loadings the formation of divanadate and two-dimensional tetrahedral polymeric vanadate species is postulated. Beside the V=O double bond and the M-O–V bonds, these species should contain additional V–O–V bonds. Furthermore, the existence of a three-dimensional dispersed polyvanadate phase with up to ﬁve overlayers is postulated (García-Bordejé et al., 2004), in which the three-dimensional (V2O5)n crystallites have an octahedral structure with the base unit VO6. The latter are reported to be less active and less selective towards ODHE than the dispersed vanadate species (Pieck et al., 2004; Liu et al., 2004). It should be noted that within this prevailing concept all vanadia species are assumed to be in the oxidation state +5. However, there are also a number of studies, in which signiﬁcant amounts of V(IV) species are found in the catalysts

3.3 Catalysts and Structure–Activity Relations

even after oxidizing treatment (Matralis et al., 1995; Enache et al., 2004; Pieck, Banares, and Fierro, 2004; Reddy and Varma, 2004; Reddy et al., 2004). This is important when “active sites” are discussed, since it is directly related to the reaction kinetics in a Mars–van Krevelen mechanism. In the following, we present results regarding the catalyst characterization and structure–activity relations. 3.3.1 Catalyst Preparation and Characterization

Structure–activity relations in heterogeneous catalysis reﬂect relations between catalytic activity and structural properties of the catalysts such as doping degree, porosity, dispersion of the active species, reducibility and acid–base properties. In order to study these for ODHE over supported vanadia catalysts a large number of samples were prepared by impregnation of γ-alumina, silica and titania supports either with VO(acac)2 as V(IV) or with NH4VO3 as V(V) precursors (Klose, 2008). The V loading was varied between 1 wt% and 16 wt%. All samples were characterized by numerous techniques like atomic absorption spectroscopy (AAS), surface area determination (BET), N2 porosimetry, differential thermal analysis and thermal gravimetry (DTA/TG), X-ray diffraction (XRD), diffuse reﬂection infrared Fourier transform spectroscopy (DRIFTS), nuclear magnetic resonance (NMR) spectroscopy of 51V, X-ray photoelectron spectroscopy (XPS), temperature-programmed reduction (TPR), temperature-programmed oxidation (TPO) and temperature-programmed desorption of pyridine (TPD). Catalytic tests were carried out under oxygen-lean and oxygen-excess conditions (0.35% and 21% O2, respectively) in the oxidation of ethane (0.7%), ethylene and CO (0.7%, 1% and 21% O2) as the expected intermediates in the reaction network. The complete experimental information is described in detail by (Klose, 2008) and provides the base for the upcoming discussion. Consistent with (Weckhuysen and Keller, 2003) it was found by XRD, DRIFTS and 51V-NMR spectroscopy that on alumina and titania vanadate monolayers are formed up to V densities of 6–7 atoms/nm2, but only 1–2 atoms/nm2 on silica. The appearance of crystalline vanadia goes parallel with a dropdown of the speciﬁc surface area by up to one order of magnitude. In the case of titania, crystalline vanadia catalyzes the conversion of anatase to rutile and leads to a collapse of the porous framework of this support material (Djerad et al., 2004; Reddy et al., 2004). In tests of the catalytic activity in ODHE under lean oxygen conditions, it was found that alumina-supported vanadia catalysts provided the highest ethylene yields among the studied supports. Ethylene yields of up to more than 20% were obtained, in the same range as reported in the literature (Le Bars et al., 1996; Argyle et al., 2002). In these experiments, at ∼35% ethane conversion, complete oxygen consumption was reached. The silica-supported catalysts were less active, with ethylene yields up to 10%. The titania-supported catalysts were found to be rather

69

70

3 Catalysis and Reaction Kinetics of a Model Reaction

Ethane conversion / %

100 0.3 % O2 0.7 % O2 21 % O2

80 60 40 20 0

Ethylene selectivity / %

100 80 60 40 20 0

Ethylene yield / %

25 20 15 10 5 0 1.7

2.4

4.8

6.1

9.5 Vanadium loading / %

Figure 3.3 Ethane conversion (upper), ethylene selectivity (center) and ethylene yield (lower) against the vanadium loading on the γ-Al2O3 for various oxygen mole fractions in the feed (0.3% Δ, 0.7% 䊐,

11.7

13.1

15.7

21% 䉫, respectively, with nitrogen as balance). The experimental conditions were MCat/ V˙ = 75 kg s/m3, T = 873 K, MCat = 0.2507 g.

active but poorly selective, so that the ethylene yields were found at the same low level. In all cases the vanadia precursor material had only minor impact on the catalytic performance; the samples prepared from NH4VO3 gave comparable results to those prepared from VO(acac)2. Due to the higher ethylene yields and the selectivity the following studies were focused on vanadia on the γ-Al2O3 support material. Figure 3.3 shows the correlation of ethane conversion and ethylene selectivity to the oxygen supply and visualizes the importance of a low oxygen concentration in the reaction: While the total conversion of ethane increases with the percentage of oxygen in the feed gas up to a vanadium loading of about 6 wt%, the selectivity towards ethylene decreases signiﬁcantly in this range. The decrease in ethane conversion above a vanadium loading of 6 wt% is due to the formation of three-dimensional vanadia crystallites, which is connected to clogging of the pores and a signiﬁcant reduction of the available surface area (from more than 160 m2/g to less than about 13 m2/g).

3.3 Catalysts and Structure–Activity Relations

These results demonstrate clearly:

•

A local low oxygen concentration and a distributed oxidant dosing should help in ODHE.

•

High vanadium loadings of the support material lead to the formation of crystalline vanadia and to a decrease in ethane conversion and ethylene production.

•

Highest selectivity towards ethylene is found for lowest vanadium loadings.

For these reasons, all following kinetic experiments were performed at low vanadia coverages. 3.3.2 Mechanistic Aspects: Correlation Between Structure and Activity

In the following, some chemical and mechanistic aspects of the catalysts in the oxidative dehydrogenation of ethane are discussed in order to answer the major question: What is the active species, and what is the reaction path? Here we focus on main aspects only. More details can be found elsewhere (Klose et al., 2007). Regarding ethylene formation from ethane over supported VOx catalysts, a Mars–van Krevelen redox mechanism is commonly accepted to describe the reaction behavior. Assuming an original vanadium oxidation state of +5 in these catalysts, the prevailing models would suggest that all vanadia species in the vanadate monolayer should contribute to the catalytic performance, resulting in comparable turnover frequencies (TOF) when normalized to the surface area of the catalyst and to the amount of vanadium deposited on the support. However, normalized TOF rate constants calculated from power law expressions of the ﬁrst order with respect to C2H6, C2H4 or CO and orders of 0.5 and zero with respect to oxygen for oxygen-lean and oxygen-excess conditions, respectively, show surprisingly that the TOF for agglomerated vanadia species (i.e., above about 6 wt% V) seems to be comparable or even higher than those of dispersed ones, apparently in contradiction to literature where the opposite order with respect to the performance of vanadates and V2O5 phases has been reported (for details see Klose et al., 2007). In addition, at vanadate coverages up to ∼6 wt% V only under oxygen-excess conditions is a constant TOF level observed, while under oxygen-lean conditions the TOF decreases with increasing V loading. These trends were discovered not only for ethylene formation but also for the deep oxidation reactions. An explanation is found when the initial vanadium oxidation states of the individual catalysts are taken into account. Based on extensive TPR and XPS experiments with fresh as well as used catalysts it was found that the dispersed vanadate monolayer phases contain only ∼30% V(V) species, the residual fraction being V(IV). This V(V) percentage cannot be enlarged even after exposure of the catalysts to air at temperatures up to 650 °C. In contrast, the catalysts with agglomerated vanadia species have an oxidation state ratio of V(V) : V(IV) = 80 : 20. It should be noted that, under time on stream in ODHE, a considerable part of the less

71

72

3 Catalysis and Reaction Kinetics of a Model Reaction

reducible agglomerated vanadia phases is converted into a kind of multilayer polyvanadate phase with reducibility comparable to the dispersed monolayer vanadates (Suchorski et al., 2005; Klose et al., 2007). It should be mentioned that in a study of the reoxidation dynamics of highly dispersed VOx species supported on γ-Al2O3 Frank et al. found a maximum vanadium oxidation state +5 at temperatures around 700 K (Frank et al., 2009). Starting from V(III), these authors observed maximum average oxidation states of only 4.3–4.5 for their catalysts at temperatures up to ∼550 K. In our studies, and for the catalysts used in the different membrane reactor experiments, reoxidation of the highly dispersed VOx to average vanadium oxidation states of more than 4.3–4.4 was not observed up to temperatures of above 900 K. For the identiﬁcation of the active V species the turnover frequencies were normalized to either the V(IV) or the V(V) fractions, respectively. A meaningful correlation is only obtained for those related exclusively to V(V): here the ethylene formation follows the expected trend, with a constant TOF level for monolayer catalysts and a decrease with the appearance of three-dimensional crystallites for both oxygen-lean and oxygen-excess conditions, respectively. This strongly suggests that the outermost V(V) species are able to catalyze oxidative dehydrogenation, while V(IV) is not active for this reaction [but is reduced by H2 to V(III) in TPR experiments]. In the attempt to ﬁnd a structural model for the catalysts, it has to be kept in mind that an average oxidation state of about 4.3, corresponding to a V(IV) : V(V) ratio of 2 : 1, could not be exceeded in the mono- and polyvanadates used herein. In consequence, two different types of V cations with different redox behavior should exist in the monolayer vanadates of our catalysts, only one of which is active. Both the existence of two types of V cations within the vanadate structure and the maximum oxidation state of 4.3 were found to be in signiﬁcant contradiction to present concepts on the nature of supported vanadate phases. Thus, a new structural model was required, which had to be consistent with previous experimental ﬁndings in literature and with all the results reported herein, as well. In this chapter we can only describe the essential idea. Details of the model and additional supporting experiments are described by (Klose et al., 2007). In this model, the ﬁrst building block is the V=O unit, the presence of which is indicated by the corresponding absorption bands in DRIFT spectra of the catalysts. Furthermore, M-O–V units should be included as the crucial sites determining performance, reducibility and acid–base properties of the catalysts since these functionalities are strongly affected by the used support. Because of the signiﬁcant support effect on ODHE activity and reducibility and the strong correlation between both, it is consequent to assign M-O–V units to the active V(V) species. As another prerequisite, the presence of 2/3 of V(IV) and 1/3 of V(V) cations has to be reﬂected in the vanadate structures. There is no indication for threedimensional growth in this coverage region, thus the possibility of core-shell structures of extremely small clusters of oxidation state +5 on the surface and +4

3.4 Derivation of a Kinetic Model

inside can be excluded. It has to be concluded that the V(IV) and V(V) cations are uniformly distributed within the overall vanadate phases. This is also supported by TEM pictures of the polyvanadate phase, which show well ordered regions with chain-like structures for the coverage regime attributed to polyvanadates and no indication for three-dimensional growth (Klose et al., 2007). The smallest unit which fulﬁlls all the requirements described above is [V3O8]3−, bound by three oxygens to the support, with one central V(V) and two adjacent V(IV) cations connected by oxide anion bridges and an additional V=O double bond on each vanadium. It is assumed that this structure represents the amorphous “isolated vanadate” species, which is predominantly formed at low V densities (<2 V atoms/nm2). However, the existence of real “monovanadates” at ultra-low V loadings cannot completely be ruled out. For the polyvanadate phase, which is predominantly formed on γ-alumina at V densities higher than 2 cations/nm2 but below the appearance of crystalline vanadia species and which is characterized by a well ordered structure in the range of tens of nanometers, chains in which a V(V) cation is followed by two V(IV) cations are proposed (Klose et al., 2007). Again, the V cations are bridged by oxygen anions. Herein, oxygen bonds to the support are assigned to the V(V) cations only, and the M-O–V(V) unit is suggested to be the active site. In this model, the ratio of 2 : 1 for V(IV) : V(V) is given, too. This polyvanadate phase exhibits reducibility similar to that of the “isolated vanadates” regarding reduction temperature and oxidation states, but differs from the latter by a lower strength of Broenstedt acidity, as was found in the experiments. These proposed structures on dispersed vanadate phases do not contradict the spectroscopic ﬁndings previously reported in literature: V=O, M–O–V and V–O–V bonds causing, for example, the various known IR and RAMAN absorptions are included. It should be remarked that the existence of V(IV)–V(V) mixed oxides like V6O13 is also known for bulk species (Weckhuysen and Keller, 2003). Although at the present state a number of questions still remain open and further research is required to conﬁrm these structural proposals, they are able to explain and understand the obtained experimental results, in contrast to other models.

3.4 Derivation of a Kinetic Model

Reaction rates are usually described by mechanistic models as a function of the concentrations of the components present in the system and adjustable free parameters as, for example, reaction rate constants, activation energies and adsorption equilibrium constants. Despite intensive research these rate laws can hardly be predicted theoretically. Therefore, a detailed kinetic modeling requires parallel experimental investigations, that is, a correlation of experimental results with proposed kinetic models followed by model discrimination (Froment, 1975; Levenspiel, 1999).

73

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3 Catalysis and Reaction Kinetics of a Model Reaction

3.4.1 Experimental 3.4.1.1 Catalyst Detailed investigations on the reaction kinetics of the ODHE were carried out with a 1.4% VOx/γ-Al2O3 catalyst. This catalyst was used later in various studies of membrane reactor concepts at laboratory scale and pilot scale. It was selected because of a sufﬁcient activity, a rather high initial selectivity to ethylene and a comparable simple and well reproducible preparation. This reference catalyst was prepared by wet impregnation of a γ-Al2O3 spherical support (Condea Chemie, Germany) with a solution of vanadyl acetylacetonate in acetone, followed by calcination at 700 °C for 4 h. The vanadium content was measured by means of AAS analysis after a microwave extraction in HNO3. The properties of the reference catalyst were:

• • •

Surface area of 184.5 m2/g (by BET analysis), Average pore diameter of 10.9 nm, Particle sizes of 0.4 mm, 1.0 mm and 1.8 mm.

This catalyst was used to derive a detailed kinetic model for the reaction network shown in Figure 3.1 based on experimental data collected in a set-up described below. 3.4.1.2 Set-Up The laboratory plant consisted of a packed-bed reactor, a catalytic afterburner and analytic equipment. Electronic mass ﬂow controllers were used to mix different feed compositions from the pure gases ethane, ethylene, CO, CO2, air and nitrogen. By means of a heated eight-port multiposition valve both the feed and the product stream were analyzed by gas chromatography with a mass selective detection and a thermal conductivity detection (GC-MSD/TCD). The laboratory-scale packed-bed reactor (inner diameter 12 mm, length 19 mm) was a quartz glass tube ﬁlled with 0.25–0.50 g catalyst. The reactants were preheated inside the reactor in an inert entrance zone. The catalyst-ﬁlled reaction zone was equipped with a thermocouple to measure the reaction temperature. In addition, two sample capillaries were placed at the inlet and the outlet to measure the concentrations of the reactants and the products, respectively. The quantitative analysis was performed with a GC-MSD/TCD, as mentioned above. First, water was removed from the samples in a Haysep column (Chrompack) and then a HP ˚ Molsieve column PLOT/Q column separated hydrocarbons and CO2. In a 5 A permanent gases and CO were separated. Finally, oxygenates were separated in a DB-FFAP column. Furthermore, the permanent gases, hydrocarbons and carbon oxides were quantiﬁed by means of a TCD. The trace components like oxygenates were detected by the MSD. The relative errors in the concentrations were estimated to be <3%.

3.4 Derivation of a Kinetic Model

75

Table 3.2 Summary of experiments performed in a laboratory packed-bed reactor for kinetic modeling and parameter estimation (Joshi, 2007).

Measurements

Total ﬂow rate V˙ (L·h−1)

Catalyst mass MCat (g)

Temperature T (°C)

Overall inlet concentrations c (vol%) C2Hx

O2

CO

CO2

C2H6 feed A1 A2 A3 A4 A5

12.05–24.12 12.05–24.12 15.05–24.12 19.18 19.18

0.2507–0.5052 0.2507–0.5052 0.2507–0.5052 0.2013 0.2013

480–570 480–570 480–570 530–620 530–620

0.6–1.2 1.2 0.7 0.3–0.8 0.3–0.8

6.0 0.2–3.0 0.4–1.0 0.67 0.67

– – – 0.28–1.22 –

– – – – 0.28–0.9

C2H4 feed B1 B2 B3 B4

12.05 12.05 19.18 19.18

0.2507 0.2507 0.2013 0.2013

480–570 480–570 480–620 480–620

0.6–1.2 1.26 0.15–1.0 0.15–1.0

6.0 0.4–4.0 1.2–6.0 1.2–6.0

– – 0.5–3.2 –

– – – 0.5–3.2

CO feed C1 C2

12.05 12.05

0.2507 0.2507

480–570 480–570

– –

6.0 0.5–2.6

0.6–1.2 1.2

– –

3.4.1.3 Procedures Preliminary experiments were devoted to evaluate possible mass transfer restrictions. For this purpose experiments with three particle sizes (0.4 mm, 1.0 mm, 1.8 mm) were conducted. To analyze the network three types of experiments using the smallest particles (0.4 mm) were performed: (group A) the oxidation of ethane, (group B) the oxidation of ethylene and (group C) the oxidation of CO (see, respectively, A1–A5, B1–B4 and C1–C2 in Table 3.2). To enable the comparison of these experiments the ratio of the catalyst mass to the total ﬂow rate was kept constant. The temperature was varied between 480 °C and 620 °C. In all experiments the feed contained oxygen from 0.2 vol% up to 6.0 vol% diluted in nitrogen. The hydrocarbons were varied between 0.15 vol% to 1.26 vol% C2H4 and C2H6 (experiments of group A and group B, respectively). Furthermore, some experiments were carried out with products (CO, CO2) mixed into the inlet stream. Moreover, the experiments of group C contained only oxygen, CO and nitrogen in the feed. Within these parameter ranges a so-called cube design (Box, Hunter, and Hunter, 1978) was applied where the effects of the following variables were studied: partial pressures of the main reactants (C2H6, C2H4, CO, respectively), the partial pressure of oxygen and the temperatures (Joshi, 2007). The experimental database consisted of about 500 observations obtained in the tubular laboratory

76

3 Catalysis and Reaction Kinetics of a Model Reaction

reactor for various feed concentrations. A summary of the conditions is given in Table 3.2. 3.4.2 Qualitative Trends

Before performing a quantitative kinetic analysis the overall performance of the catalyst and the inﬂuence of mass transfer resistances were evaluated qualitatively. 3.4.2.1 Overall Catalyst Performance Here, selected trends regarding the conversion and selectivity as a function of temperature are shown. The results presented were obtained for a ﬂow rate of 12.05 L/h (MCat/V˙= 75 kg s/m3). Figure 3.4 illustrates an increase of ethane conversion and CO selectivity with increasing temperature. In contrast, ethylene selectiv-

20

100

Ethylene selectivity / %

Ethane conversion / %

95 15

10

5

90 85 80 75 70 65

0 450

475

500 525 550 Catalyst temperature /°C

60 450

575

30

475

500 525 550 Catalyst temperature /°C

575

30

CO2 selectivity / %

CO selectivity / %

25 25

20

15

20 15 10 5

10 450

475

500

525

550

575

Catalyst temperature /°C

Figure 3.4 Illustration of the performance of the catalyst characterization: ethane conversion (upper left), ethylene selectivity (upper right), CO selectivity (lower left) and CO2 selectivity (lower right) as a function of

0 450

475

500

525

550

Catalyst temperature /°C

temperature. Experimental conditions: MCat/V˙= 75 kg s/m3, 1.22 vol% ethane and 1.67 vol% oxygen (balance nitrogen), MCat = 0.2507 g.

575

3.4 Derivation of a Kinetic Model

77

ity decreases with temperature. The formation of CO2 remains constant in the observed temperature region. Selectivities of ethylene, CO and CO2 were found at 540 °C to be 80.5%, 8.4% and 11.1%, respectively. In general, the catalyst was very selective towards ethylene for lower temperatures. These ﬁndings are in a good agreement with publications from other authors (e.g., Argyle et al., 2002; Grabowski, 2006; Waku et al., 2003). 3.4.2.2 Evaluation of Intraparticle Mass Transfer Limitations For investigating reaction kinetics the experimental data should not be inﬂuenced by mass transfer limitations to allow transferring results to other reactor concepts. To evaluate the inﬂuence of possible mass transfer limitations additional experiments were performed with two different catalyst particle sizes (1.0 mm and 1.8 mm) in the range of 580 °C to 670 °C. A mixture of 2.16 vol% ethane and 2.10 vol% oxygen (balance nitrogen) was fed to the reactor. Measured overall reaction rates of ethane and of ethylene with respect to the temperature are shown in Figure 3.5. The overall consumption of ethane is for the conditions mentioned not inﬂuenced by mass transfer limitations. Regarding ethylene

20

11

18

10

16

9

14

8 RC H / (mol/kg h) 2 4

RC H / (mol/kg h) 2 6

1 mm 1.8 mm

12

7

10

6

8

5

6

4

4

3 580

600

620

640

Catalyst temperature /°C

660

680

580

600

620

640

Catalyst temperature /°C

Figure 3.5 Overall reaction rates of ethane (left) and ethylene (right) against catalyst temperature for catalyst particles of 1 mm (Δ) and 1.8 mm (䊐) size, respectively. The feed consisted of 2.16 vol% ethane and 2.1 vol% oxygen (balance nitrogen).

660

680

78

3 Catalysis and Reaction Kinetics of a Model Reaction

formation, lower rates were observed with the 1.8 mm particles than with the 1 mm particles. This result led to the decision to perform the experiments used in the kinetic analysis exclusively with the smallest catalyst particle size (0.4 mm). 3.4.3 Quantitative Evaluation 3.4.3.1 Simpliﬁed Reactor Model and Data Analysis To extract kinetic data from measurements performed in tubular reactors, in principle an integration of the mass and energy balances is required. This allows matching theoretical and experimental outlet concentrations. If, however, conversion and deviations from isothermal conditions are low, a much simpler analysis can be applied. In this case averaged reactor concentrations can be determined for all components from the arithmetic means of the inlet and outlet concentrations. Further, component speciﬁc overall reactions rates Ri can be estimated using the following simpliﬁed steady-state mass balance:

Ri =

(ci ,in − ci ,out )V , MCat

(3.10)

where ˜ ci,in and ˜ ci,out are inlet and outlet concentrations, respectively, V˙ is the volumetric ﬂow rate, MCat is the mass of catalyst. The overall reaction rate Ri as used here has the dimension: mol/(kgCat h). In accordance with the reaction network under investigation the overall rates Ri are linked to the individual reaction rates rj using the corresponding stoichiometric coefﬁcients vij, M

Ri = ∑ ν ijr j

(3.11)

j

The approach described was used to analyze the subset of the available experimental data characterized by ethane conversions below 20% providing ﬂat temperature proﬁles and almost isothermal conditions in the reactor. The remaining experiments yielding larger conversions were used for model validation, as described in Section 3.4.4. 3.4.3.2 Kinetic Models The structure of suitable rate equations – the models of rj(T, ˜ c1, … , ˜ cN) – is not known a priori, although physico-chemical insight and preliminary knowledge about the mechanism of the involved reaction steps limit the spectrum of possible models (Froment, 1975). Beside other formulations, the Langmuir–Hinshelwood and Hougen–Watson (LHHW) models (Hougen and Watson, 1943) and the Mars– van Krevelen (Mars and van Krevelen, 1954) model are widely known and used in heterogeneous catalytic processes. The latter is especially suited for catalytic oxidations, such as the oxidative dehydrogenation of ethane (Reaction 3.1). As mentioned above, it assumes that oxygen is provided by the lattice of the solid

3.4 Derivation of a Kinetic Model

catalyst and the reduced catalyst is then re-oxidized by gas phase oxygen. The model reads: r1 =

kredcC2Hn +2 kox cOβ 2 , kredcC2Hn +2 + kox cOβ 2

(3.12)

where β is the order with respect to oxygen. It is set to β = 0.5, regarding the assumption of a dissociative oxygen adsorption. The well known LHHW models assumes reactants and products can be adsorbed on the catalyst surface and that all the elementary steps of an overall reaction are close to the equilibrium except the rate-determining step (e.g., the surface reaction). Depending on the decisions of the rate-determining step different formulations of LHHW models are possible. Details regarding the model formulation can be found in the literature, for example, (Hougen and Watson, 1947; Froment and Bischoff, 1979). Usually various possible model formulations are tested in a regression analysis. Afterwards model discrimination is applied. Here, for Reactions 3.2 to 3.5 various LHHW models were derived based on different assumptions on the mechanism and the rate-determining step of the elementary reactions (Yang and Hougen, 1950; Doraiswamy and Sharma, 1984; Joshi, 2007). 3.4.3.3 Parameter Estimation The free parameters of the various kinetic models evaluated were the reaction rate constants, the activation energies and the adsorption equilibrium constants. Initial estimates of the adsorption equilibrium constants were extracted from the literature (Argyle et al., 2002). All initial estimates were reﬁned in a regression analysis using a Levenberg–Marquardt algorithm (Moré, 1978) minimizing the following objective function:

OF =

∑ i

2

exp ⎛ R − R mod ⎞ ∑k ⎜⎝ ik R exp ik ⎟⎠ ik

N components N exp

(3.13)

Based on the magnitude of the OF values obtained model discrimination was performed and a model was identiﬁed, which is described in the next section. 3.4.4 Suggested Simpliﬁed Model

The oxidative dehydrogenation of ethane to ethylene was quantiﬁed using a reaction network, which was derived from experiments on oxidation of ethane and ethylene and CO as intermediates. The reaction network consists of ﬁve partial reactions: (r1) ethane to ethylene and water, (r2) ethane to carbon dioxide and water, (r3) ethylene to carbon monoxide and water, (r4) ethylene to carbon dioxide and water and (r5) carbon monoxide to carbon dioxide (Figure 3.1, Equations 3.1–3.5). To quantify the rates of the Reactions 3.1 to 3.5 for a VOx/γ-Al2O3 catalyst with 1.4% V the expressions summarized in Table 3.3 are suggested. Reaction 3.1 is described by a Mars–van Krevelen mechanism. Reactions 3.2

79

80

3 Catalysis and Reaction Kinetics of a Model Reaction Table 3.3 Suggested kinetic model of the oxidative dehydrogenation of ethane to ethylene on

a VOx/γ-Al2O3 catalyst with 1.4% V. The corresponding parameters are listed in Table 3.4. kred cC2H6 kox cO0.25 kred cC2H6 + kox cO0.25 k2 (T )K C2H6 cC2H6 K O0.52 cO0.25 r2 = (1 + K C2H6 cC2H6 + K CO2 cCO2 ) (1 + K O0.52 cO0.25 ) r1 = k1 (T )

r3 =

k3 (T )K C2H4 cC2H4 K O0.52 cO0.25 (1 + K C2H4 cC2H4 + K COcCO ) (1 + K O0.52 cO0.25 )

r4 =

k4 (T )K C2H4 cC2H4 K O0.52 cO0.25 (1 + K C2H4 cC2H4 + K CO2 cCO2 ) (1 + K O0.52 cO0.25 )

r5 =

k5 (T )K COcCOK O0.52 cO0.25 2 (1 + K COcCO + K O0.52 cO0.25 + K CO2 cCO2 )

Table 3.4 Optimized parameter values for the favorite kinetic model as presented in Table 3.3.

k value [mol (kg h)−1]

E value (kJ mol−1)

K value (L mol−1)

k1,0 = 1.0

EA,1 = 94

K C2H6 = 4770

k2,0 = 1.6 × 107

EA,2 = 114

K C2H4 = 3026

k3,0 = 2.0 × 104 k4,0 = 1.0 × 103 k5,0 = 1.1 × 107 kred = 4.3 × 109 L (kg h)−1

EA,3 = 51 EA,4 = 51 EA,5 = 118 kox = 1.1 × 108 mol0.5L0.5 (kg h)−1

KCO = 3456 K CO2 = 3234 −1 K O2 = 1003 L0.5 (mol 0.5 )

to 3.4 are described by two-site Langmuir–Hinshelwood equations. In contrast Reaction 3.5 is quantiﬁed by a Langmuir–Hinshelwood mechanism based on single-site competitive adsorption. In each kinetic equation the oxygen reaction order is 0.5, which assumes that oxygen participates in all reactions in dissociated form. The temperature dependencies of the ﬁve pre-factors kj are described by Arrhenius’ law: )] k j = k j ,0 exp [ −E A , j (RT

j = 1 ... 5

(3.14)

To reduce the number of free model parameters and to allow for convergence of the optimization procedure the adsorption equilibrium constants Ki were assumed not to depend on temperature. All parameters estimated are summarized in Table 3.4. Finally, in order to validate the derived kinetic model with the available experiments leading to conversions above 20%, numerical simulations were performed using a non-isothermal pseudo-homogeneous one-dimensional plug-ﬂow model (Froment and Bischoff, 1979; Elnashaie and Elshishini, 1994) implemented in

3.4 Derivation of a Kinetic Model Ethylene yield 30

80

25 Experiment

Experiment

Ethane conversion 100

60 40 20

20 15 10 5

0

0 0

20

40 60 Model

80

100

0

5

10

25

30

CO2 yield

CO yield 35

70

30

60

25

50 Experiment

Experiment

15 20 Model

20 15

40 30

10

20

5

10

0

3

30 kg s/m 3 100 kg s/m 200 kg s/m3

0 0

5

10

15 20

25

30

35

Model

Figure 3.6 Comparison of experimentally determined and modeled ethane conversion (upper left), ethylene yield (upper right), CO yield (lower left) and CO2 yield (lower right)

0

10 20

30

40

50 60

70

Model

over VOx/γ-Al2O3 catalyst for three experimental conditions: MCat/V˙= 30 kg s/m3 (Δ), 100 kg s/m3 (䉫) and 200 kg s/m3 (䊐).

COMSOL Multiphysics and PROMOT/DIVA (see also Chapter 2). Theoretical reactor outlet concentrations were generated and compared with the corresponding data. Figure 3.6 compares experimental and theoretical conversion, yield and selectivity data. The ﬁrst subset of theoretical data (conversion <20%) is based on the application of the averaged reactor concentrations in combination with the determined rate laws. The second subset (>20%) is based on the numerical simulations of the more detailed reactor model. A relatively good agreement for the whole parameter range studied can be observed. More detailed results of the mentioned study are not given here and the interested reader is referred to the literature (Joshi, 2007). Despite the relative large data basis acquired and the systematic model generation and discrimination approach followed, the kinetic model suggested does not represent a description of the real reaction mechanism. It rather can be considered as a formal description of the reaction network valid in the temperature and

81

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3 Catalysis and Reaction Kinetics of a Model Reaction

concentration space covered. This kinetic model is valid for hydrocarbon concentrations between 0.15% and 1.0%, for oxygen concentrations between 0.15% and 20.5% and for a temperature range from 450 °C to 650 °C. It should be of value for the analysis and design of conventional and new reactor concepts as, for example, the membrane reactors of the distributor type considered in this book (Chapters 4–8).

Special Notation not Mentioned in Chapter 2 Latin Notation

EA,j

J/mol

kj kj,0 kox

mol/(kg s) mol/(kg s) mol0.5 L0.5 /(kg s)

kred

L/(kg h)

Ki

L/mol

MCat OF Ri

kg mol/kg s

V˙

m3/s

activation energy of reaction j rate constant of reaction j pre-factor of reaction j rate constant of oxidation step in Mars–van Krevelen mechanism rate constant of reduction step in Mars–van Krevelen mechanism adsorption equilibrium constant of component i mass of catalyst objective function overall reaction rate of component i volumetric ﬂow

Greek Notation

α β

reaction rate order with respect to hydrocarbon reaction rate order with respect to oxygen

References Argyle, M.D., Chen, K., Bell, A.T., and Iglesia, E. (2002) Effect of catalyst structure on oxidative dehydrogenation of ethane and propane on aluminasupported vanadia. J. Catal., 208, 139–149. Banares, M.A. (1999) Supported metal oxide and other catalysts for ethane conversion: a review. Catal. Today, 51, 319–348.

Bhasin, M.M., McCain, J.H., Vora, B.V., Imai, T., and Pujadó, P.R. (2001) Dehydrogenation and oxydehydrogenation of parafﬁns to oleﬁns. Appl. Catal. A Gen., 221, 397–419. Blasco, T., and López Nieto, J.M. (1997) Oxidative dehydrogenation of short chain alkanes on supported vanadium oxide

References catalysts. Appl. Catal. A Gen., 157, 117–142. Box, G.E.P., Hunter, W.G., and Hunter, J.S. (1978) Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building, John Wiley & Sons, Inc. Busca, G. (1996) Infrared studies of the reactive adsorption of organic molecules over metal oxides and of the mechanisms of their heterogeneouslycatalyzed oxidation. Catal. Today, 27, 457–496. Cavani, F., and Triﬁro, F. (1999) Selective oxidation of light alkanes: interaction between the catalyst and the gas phase on different classes of catalytic materials. Catal. Today, 51, 561–580. Chary, K.V.R., Kishan, G., Kumar, C.P., and Sagar, G.V. (2003) Structure and catalytic properties of vanadium oxide supported on alumina. Appl. Catal. A Gen., 246, 335–350. Dai, H.X., and Au, C.T. (2002) The oxidative dehydrogenation of ethane to ethene. Curr. Topics Catal., 3, 33–80. Deo, G., Wachs, I.E., and Haber, J. (1994) Supported vanadium oxide catalysts: molecular structural characterization and reactivity properties. Crit. Rev. Surf. Chem., 4, 141–187. Djerad, S., Tifouti, L., Crocoll, M., and Weisweiler, W. (2004) Effect of vanadia and tungsten loadings on the physical and chemical characteristics of V2O5-WO3/TiO2 catalysts. J. Mol. Catal. A Chem., 208, 257–264. Doraiswamy, L.K., and Sharma, M.M. (1984) Heterogeneous Reactions Analysis, Examples and Reactor Design: Gas-Solid and Solid-Solid Reactions, John Wiley & Sons, Inc. Elnashaie, S.S.E.H., and Elshishini, S.S. (1994) Modelling, Simulation, and Optimization of Industrial Fixed Bed Catalytic Reactors, CRC Press. Enache, D.I., Bordes-Richard, E., Ensuque, A., and Bozon-Verduraz, F. (2004) Vanadium oxide catalysts supported on zirconia and titania: I. Preparation and characterization. Appl. Catal. A Gen., 278, 93–102. Frank, B., Fortrie, R., Hess, Ch., Schlögl, R., and Schomäcker, R. (2009) Reoxidation dynamics of highly dispersed VOx species

supported on γ-alumina. Appl. Catal. A Gen., 353, 288–295. Froment, G.F. (1975) Model discrimination and parameter estimation in heterogeneous catalysis. AIChE J., 21, 1041–1057. Froment, G.F., and Bischoff, K.B. (1979) Chemical Reactor Analysis and Design, John Wiley & Sons, Inc. García-Bordejé, E., Lázaro, J., Moliner, R., Galindo, J.F., Sotres, J., and Baro, A.M. (2004) Morphological characterization of vanadium oxide supported on carboncoated monoliths using AFM. Appl. Surf. Sci., 228, 135–142. Grabowski, R. (2006) Kinetics of oxidative dehydrogenation of C2–C3 alkanes on oxide catalysts. Catal. Rev., 48, 199–268. Grasselli, R.K. (1999) Advances and future trends in selective oxidation and ammoxidation catalysis. Catal. Today, 49, 141–153. Grzybowska-Swierkosz, B. (1999) Active centres on vanadia-based catalysts for selective oxidation of hydrocarbons. Appl. Catal. A Gen., 157, 409–420. Haber, J., Witko, M., and Tokarz, R. (1999) Vanadium pentoxide I. Structures and properties. Appl. Catal. A Gen., 157, 3–22. Hougen, O.A., and Watson, K.M. (1943) Solid catalysts and reaction rates. Ind. Eng Chem., 35 (5), 529–541. Hougen, O.A., and Watson, K.M. (1947) Chemical Process Principles: Part 3. Kinetics and Catalysis, John Wiley and Sons, Inc. Joshi, M. (2007) Statistical analysis of models and parameters in chemical and biochemical reaction networks, Dissertation, Otto von Guericke University. Klose, F. (2008) Structure-Activity Relations of Supported Vanadia Catalysts and the Potential of Membrane Reactors for the Oxidative Dehydrogenation of Ethane, Habilitation thesis, Otto von Guericke University Magdeburg. Klose, F., Joshi, M., Hamel, C., and Seidel-Morgenstern, A. (2004) Selective oxidation of ethane over a VOx/γ-Al2O3 catalyst – investigation of the reaction network. Appl. Catal. A Gen., 260, 101–110. Klose, F., Wolff, T., Lorenz, H., SeidelMorgenstern, A., Suchorski, Y., Piórkowska, M., and Weiss, H. (2007)

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3 Catalysis and Reaction Kinetics of a Model Reaction Active species on γ-alumina-supported vanadia catalysts: nature and reducibility. J. Catal., 247, 176–193. Le Bars, J., Védrine, J.C., Auroux, A., Pommier, B., and Pajonk, G.M. (1992) Calorimetric study of vanadium pentoxide catalysts used in the reaction of ethane oxidative dehydrogenation. J. Phys. Chem., 96, 2217–2221. Le Bars, J., Auroux, A., Forissier, M., and Vedrine, J.C. (1996) Active Sites of V2O5/γ-Al2O3Catalysts in the Oxidative Dehydrogenation of Ethane. J. Catal., 162, 250–259. Levenspiel, O. (1999) Chemical Reaction Engineering, 3rd edn, John Wiley & Sons Inc. Liu, Y.-M., Cao, Y., Yi, N., Feng, W.-L., Dai, W.-L., Yan, S.-R., He, H.-Y., and Fan, K.-N. (2004) Vanadium oxide supported on mesoporous SBA-15 as highly selective catalysts in the oxidative dehydrogenation of propane. J. Catal., 224, 417–428. Magagula, Z., and van Steen, E. (1999) Time on stream behaviour in the (amm) oxidation of propene/propane over iron antimony oxide: cyclic operation. Catal. Today, 49, 155–160. Mamedow, E.A., and Cortés Corberán, V. (1995) Oxidative dehydrogenation of lower alkanes on vanadium oxide-based catalysts. The present state of the art and outlooks. Appl. Catal. A Gen., 127, 1–40. Mars, P., and van Krevelen, D.W. (1954) Oxidations carried out by means of vanadium oxide catalysts. Chem. Eng. Sci. (Spec. Suppl.), 3, 41–59. Matralis, H.K., Ciardelli, M., Ruwet, M., and Grange, P. (1995) Vanadia catalysts supported on mixed TiO2-Al2O3 supports. Effect of composition on the structure and acidity. J. Catal., 157, 368–379. Moré, J.J. (1978) The Levenberg-Marquardt algorithm: Implementation and theory, Numerical Analysis, 630/1978, pp. 105–116, in Lecture Notes in Mathematics, Springer.

Oyama, S.T., and Somorjai, G.A. (1990) Effect of structure in selective oxide catalysis: oxidation reactions of ethanol and ethane on vanadium oxide. J. Phys. Chem., 94, 5022–5028. Pieck, C.L., Banares, M.A., and Fierro, J.L.G. (2004) Propane oxidative dehydrogenation on VOx/ZrO2 catalysts. J. Catal., 224, 1–7. Reddy, B.M., Ganesh, I., and Khan, A. (2004) Stabilization of nanosized titania-anatase for high temperature catalytic applications. J. Mol. Catal. A Chem., 223, 295–304. Reddy, E.P., and Varma, R.S. (2004) Oxidative dehydrogenation of short chain alkanes on supported vanadium oxide catalysts. J. Catal., 221, 93–104. Suchorski, Y., Rihko-Struckmann, L., Klose, F., Ye, Y., Alandjiyska, M., Sundmacher, K., and Weiss, H. (2005) Evolution of oxidation states in vanadiumbased catalysts under conventional XPS conditions. Appl. Surf. Sci., 249, 231–237. Tóta, A., Hamel, C., Thomas, S., Joshi, M., Klose, F., and Seidel-Morgenstern, A. (2004) Theoretical and experimental investigation of concentration and contact time effects in membrane reactors. Chem. Eng. Res. Des., ISMR3-CCRE18, 82, 236–244. Waku, T., Argyle, M., Bell, A., and Iglesia, E. (2003) Effects of O2 concentration on the rate and selectivity in oxidative dehydrogenation of ethane catalyzed by vanadium oxide: implications for O2 staging and membrane reactors. Ind. Eng. Chem. Res., 42, 5462–5466. Weckhuysen, B.M., and Keller, D.E. (2003) Chemistry, spectroscopy and the role of supported vanadium oxides in heterogeneous catalysis. Catal. Today, 78, 25–46. Yang, K.H., and Hougen, O.A. (1950) Determination of mechanism of catalyzed gaseous reactions. Chem. Eng. Prog., 46, 146–157.

85

4 Transport Phenomena in Porous Membranes and Membrane Reactors Katya Georgieva-Angelova, Velislava Edreva, Arshad Hussain, Piotr Skrzypacz, Lutz Tobiska, Andreas Seidel-Morgenstern, Evangelos Tsotsas, and Jürgen Schmidt 4.1 Introduction

Membrane reactors offer the possibility to integrate dosing, separation and reaction processes in a single apparatus. Their efﬁcient operation depends on the effectiveness of the catalyst and the corresponding reaction kinetics as well as on the transport processes in the reactor. The diffusive and convective mass and energy transfer can be systematically inﬂuenced by the reactor geometry, the membrane morphology and the operation conditions. Hence, there is a high optimization potential for these reactors. Due to the large number of parameters, the numerical simulation is increasingly used for reactor sizing and design. The applied models and tools for this purpose are presented in Chapter 2, where different modeling depths are taken into account. Chapter 3 provides details about the kinetics of an example reaction (oxidative dehydrogenation of ethane), which are necessary for the study of the catalysts, membranes and processes in the framework of this project. The aim of the current chapter is the analysis of the transport phenomena, in particular the superposition of convection and diffusion processes. It focuses on ﬁxed-bed or packed-bed reactors (PBR), packed-bed membrane reactors (PBMR) and catalytic membrane reactors (CMR), which are investigated numerically by a pseudo-homogeneous model approach. Concerning the superposition of convective and diffusive processes, some aspects of the numerical solution of the corresponding differential equations are discussed from a mathematical point of view in Section 4.2. The complexity of the simulation model and the numerical effort depend on the model dimension and especially on the manner of description of the velocity proﬁles. Through meaningful simpliﬁcations in the modeling, based on a balance between expenses and beneﬁts, computing effort can often be signiﬁcantly reduced. Plug ﬂow conditions or developed velocity proﬁles are frequently used as model assumptions. For example in PBRs, developed velocity proﬁle can be reliably used for the momentum analysis without great deviation to the full-order model, (Hein, 1999), due to the setting of this proﬁle after a very short entrance length. But, no developed proﬁle can be obtained in the membrane reactor due to Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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4 Transport Phenomena in Porous Membranes and Membrane Reactors

the axial reactant dosing. Only a few publications consider this phenomenon in detail. Therefore, Section 4.3 deals with the particularities of the velocity ﬁelds in membrane reactors and focuses on:

• • •

The need to consider compressibility in the equation of motion The developing ﬂow behavior of the ﬂuid and the possibilities of formulating a scaled velocity proﬁle, independent from the reactor length The effect of the pressure drop in the reactor tube on the axial dosing (Hamel, 2008).

Another studied point is the analysis of the transport processes in the membranes. In this work, two types of membrane (Al2O3 membranes, sintered metals) are considered experimentally and theoretically. There are different transport mechanism in these two types of membrane and an experimental identiﬁcation of the effective morphological and transport coefﬁcients is essential for a correct model description. The experimental set-up and the analysis of the results based on the dusty gas model (DGM) are brieﬂy described and discussed in Section 4.4. Furthermore the summarized results for the different membrane layers are used for a modeling study in this chapter as well as in Chapters 5 and 8. The application of the derived DGM model parameters in CFD simulations requires a link between the different approaches and subsequently the model validation. The implementation procedure is discussed regarding a 2-D model. The combination of convective and diffusive transport in the different reactor zones and in conjunction with the reaction kinetics is the subject of Section 4.5. Ethane and products can diffuse through the membrane into the shell side, causing an undesired mass loss. To avoid or limit this process, both operating conditions like mass ﬂux through the membrane and membrane structure parameters like pore diameter, thickness and ε/τ ratio can be used. Due to the smaller mass ﬂux through the membrane in a CMR compared to a PBMR, the risk of product loss is much greater in a CMR. The increase in the mass ﬂux of a mixture of inert gas/oxygen through the membrane can be kept only in narrow limits because ethane is transported into the catalyst layer only by diffusion and a reaction inhibition can arise. The developing concentration proﬁles in the reactor tube and the oxygen dosage determine the activity of the catalyst layer. In a PBMR, oxygen reaches the catalyst particles at the reactor axis only after a given length, so that near the inlet an inactive region is formed. A sensible matching of the reaction and transport processes is required and an optimal operation of the membrane reactor can be achieved only by using appropriate parameters. Furthermore, an analysis of the inﬂuence of the membrane geometry and structural parameters as well as of operating conditions is performed for the CMR in Section 4.6. Yield and selectivity of the desired product are sensitively affected in this reactor by the transport processes. A few results from an experimental investigation were achieved for the CMR, revealing that the preparation of the catalytic active layer did not provide a sufﬁcient thickness. Therefore, numerical simulations were carried out to evaluate the reactor performance. The results

4.2 Aspects of Discretizing Convection-Diffusion Equations

obtained contribute to a better understanding of the coupled processes occurring in the reactor.

4.2 Aspects of Discretizing Convection-Diffusion Equations

The balance equations for the energy and species derived in Chapter 2 are of the convection–diffusion type in which convection is often dominant due to the smallness of thermal conductivity and diffusion coefﬁcients, respectively. This causes several difﬁculties when solving these equations numerically; for an overview see (Roos, Stynes, and Tobiska, 2008). The problems and basic ideas to handle them can be illustrated for the simple convection–diffusion equation: −DΔy + v ⋅∇y = f

in Ω,

y = yD

on ΓD , D

∂y = 0 on Γ N , ∂n

(4.1)

where y denotes the concentration of a chemical species, D is the diffusion coef ﬁcient, v is the velocity ﬁeld, f is a source term, Ω is a two- or three-dimensional domain and yD is the concentration given at the Dirichlet part ΓD of the boundary, and ΓN is the Neumann outﬂow part of the boundary. The numerical results of a standard Galerkin and an upwind approach for the 2-D test case on a 33 × 33 cartesian triangular grid corresponding to 1089 degrees of freedom are presented for the data D = 10−7, f = 0, v = [8xy (1 − x ) , − 4 (2x − 1) (1 − y 2 )], ΓN = {(x, y) ∈ ∂Ω : 1/2 < x < 1, y = 0}, ΓD = ∂Ω\ΓN, yD = 1 for 1/4 ≤ x ≤ 1/2, y = 0 and 0 ≤ y ≤ 1, x = 1, yD = 0 otherwise on ΓD. The in- and out-ﬂow parts can be seen in vector plot of the velocity, see Figure 4.1. As one can see in Figure 4.2, the solution obtained by

Figure 4.1

Velocity ﬁeld.

87

88

4 Transport Phenomena in Porous Membranes and Membrane Reactors

Figure 4.2

Galerkin solution (left), upwind solution (right).

the standard Galerkin ﬁnite element method exhibits spurious nonphysical oscillations and is therefore completely useless. Applying a ﬁrst-order upwind ﬁnite element method improves the solution quality considerably but the sharp inﬂow front at x = 1/4, y = 0 is smeared out. The consistent streamline–diffusion method has been developed for convection–diffusion reaction problems in order to combine stability with high accuracy, see for example, (Roos, Stynes, and Tobiska, 2008). This type of stabilization is based on adding weighted residuals to: SSD ( y, ψ ) = ∑ τ K ( −DΔy + v ⋅∇y − f , v ⋅∇ψ )K (4.2) K

the standard Galerkin formulation where the summation goes over all ﬁnite element cells K and τK denotes a user chosen positive stabilization parameter. However, applied to systems of convection–diffusion reaction equations additional nonphysical couplings are introduced by the consistency requirement. Therefore, a new stabilization method based on local projections has been developed, mathematically investigated and successfully implemented (Matthies, Skrzypacz, and Tobiska, 2007; Matthies, Skrzypacz, and Tobiska, 2008). Instead of weighted residuals only weighted ﬂuctuations κh(∇y) are added to the Galerkin formulation, resulting in a stabilizing term of the form: SLP ( y, ψ ) = ∑τ K (κ h ( ∇y ) ,κ h ( ∇ψ ) )K .

(4.3)

K

Applied to systems, such symmetric stabilization terms avoid nonphysical additional couplings between the balance equations and lead to block diagonal matrices in the algebraic system. The stabilizing effect of the local projection stabilization (LPS) can clearly be seen in Figure 4.3 (left). Compared to the Galerkin method the oscillations are damped and localized in the direct neighborhood of sharp fronts. This stability behavior similar to the streamline–diffusion method has been mathematically established by (Knobloch and Tobiska, 2008), however the LPS does not introduces artiﬁcial couplings when applied to systems of equations.

4.3 Velocity Fields in Membrane Reactors

Figure 4.3

LPS solution (left), LPS solution with additional shock-capturing (right).

Although the new developed LPS combines good stability properties with high accuracy, it does not satisfy – just like the streamline–diffusion stabilization – the discrete maximum principle. Thus, there is no guarantee that physical properties like the positivity and boundedness of the solution of the balance equations are preserved in the discrete case. To improve the quality of the discrete solution the stabilized schemes can be modiﬁed by adding a nonlinear shock-capturing term. In Figure 4.3 (right) this improvement can be clearly seen for an edge-oriented shock-capturing term. The numerical results for the LPS and LPS with shock capturing have been computed for an enriched piecewise linear ﬁnite element method on a triangular mesh and a piecewise constant projection space, cf. (Matthies, Skrzypacz, and Tobiska, 2008). The new approach has been successfully applied to the various coupled transport ﬂow problems.

4.3 Velocity Fields in Membrane Reactors

The numerical effort of the simulation mainly depends on the used model for the velocity ﬁeld. Often, the velocity and pressure ﬁelds are governed by the Navier– Stokes equations which can be formulated for a compressible or incompressible ﬂuid. In order to estimate the need for a compressible formulation, the inﬂuence of the gas compressibility on the yield and transmembrane pressure difference was investigated in preliminary studies. For compressible ﬂows, the gas density is a function of the pressure changes in the reactor; otherwise the density depends only on the predeﬁned operating pressure. For membranes with a thin catalyst layer (3 μm thickness), minor variations in the ethylene yield and transmembrane pressure drop are observed varying the SS/TS = V˙SS/V˙TS ratio. In these cases, an incompressible formulation (ρ, η = const) of the momentum balances equation is sufﬁcient to study the transport phenomena.

89

4 Transport Phenomena in Porous Membranes and Membrane Reactors

yield of ethylene [%]

yield of ethylene [%] p

3μm thickness

4

compressible incompressible 3

2

1

10μm thickness

12

compressible incompressible 9

6

3

0

0 0

2

4

6

8

0

10

2

3µm thickness

x 104

8

4

6

8

10

SS/TS [-]

SS/TS [-] 12

compressible incompressible

10µm thickness

x 104

compressible incompressible

6

9

Δp [Pa]

Δp [Pa]

90

4

2

6

3

0

0

0

2

4

6

SS/TS [-]

8

10

0

2

4

6

8

10

SS/TS [-]

Figure 4.4 Inﬂuence of SS/TS on the ethylene yield and transmembrane pressure difference for 3 and 10 μm thicknesses of the catalyst layer for GHSV = 27 736 L/h, T = 620 °C.

However, increasing the membrane layer thickness as well as reducing the pore diameter and porosity to tortuosity ratio, it is expected that the gas compressibility strongly inﬂuences the reactor performance. As shown in Figure 4.4, where simulations are carried out also with a 10 μm catalyst layer, obvious differences appear in the yield values, especially for high-volume ﬂow rates at the shell inlet. The deviations of the transmembrane pressure drop are signiﬁcantly larger and reach 26%. Therefore, obtaining results for the transmembrane pressure drop under the given conditions requires simulations based on compressible ﬂuid behavior. The transport processes in the reactor are inﬂuenced by the different types of velocity proﬁles (plug-ﬂow, parabolic proﬁle, etc.) used and the development of the ﬂow behavior. In particular, for large entrance zones a detailed computation of the velocity ﬁelds is needed and a fully developed velocity proﬁle cannot be assumed. This is also the case in membrane reactors of the distributor type where a developed velocity proﬁle cannot be expected due to the axial reactant dosing. Based on the combination of reactor and membrane functions, there are differences in the formation of velocity, concentration and temperature proﬁles compared to conventional reactors. This is demonstrated in the following example.

4.3 Velocity Fields in Membrane Reactors

The axial and radial velocity proﬁles in two types of CMR, calculated with the 2-D model under isothermal conditions, are compared and presented in Figure 4.5 in dimensionless form. The inlet velocity at the tube side and the reactor diameter are used as a scale basis. The velocity ﬁelds are calculated on the basis of macroscopic average superﬁcial values. In the ﬁrst type reactor, the tube is empty and, in the second one, the tube is ﬁlled with inert particles. By these simulations, identical operating conditions are deﬁned for both reactors. In the case of CMR without packed bed, parabolic proﬁles of axial velocity are characteristic for the laminar ﬂow in the channels. If a packed bed is posed in the reactor tube, the velocity proﬁles are formed by a sink in the momentum equations. The pressure loss is described by usage of the Ergun equation, Equation 2.21, and as a result a ﬂat proﬁle of the axial velocity is observed. Furthermore, a radial dependence of bed porosity is considered and calculated according to Equation 2.22. At a low tube : particle diameter ratio, the consideration of the porosity proﬁle in the reactor has a strong inﬂuence not only on the ﬂow maldistribution, but also on the concentration and temperature proﬁles (Keil, 2007). The porosity rises rapidly close to the membrane wall and the axial velocity increases signiﬁcantly causing undesirable ﬂow channeling, (Schlünder and Tsotsas, 1988). In the membrane, the values of the axial velocity decrease signiﬁcantly as a result of the low permeability coefﬁcients of the porous media and they approach zero for both reactors. Moreover, a convective radial ﬂow through the membrane is characteristic for the membrane reactors of the distributor type. The development of the radial velocity proﬁle depends on the intensity and direction of the pressure gradients. The axial pressure gradients in the annulus, the packed bed or the tube are small compared to the pressure drop between the tube and shell side in the considered cases. Consequently, qualitative identical radial velocity proﬁles with the reactor length are obtained in both CMRs. In case of a signiﬁcant pressure loss caused by the packing, an inﬂuence of the velocity ﬁeld on the axial distribution of the dosing is given (Hamel, 2008). The radial velocity proﬁles go in both reactors through a minimum. This occurs in the CMR with a packed bed in the vicinity of the wall. After that the radial velocity increases linearly towards the core. In the CMR, the minimum lies near the core, caused by the well known laminar proﬁle. If the dimensionless axial velocities in both reactors are scaled to the local average cross-sectional velocity in reactor tube, an uniform self-similar distribution can be predicted along the reactor, see Figure 4.5e,f. In the PBMR, the similar proﬁles are observed after a very short distance, whereas the ﬂow in the CMR needs to develop along about 10% of the reactor length. Figure 4.6 shows the development of the scaled maximal velocity as a function of the axial coordinate of the CMR. The different velocity distributions in the case of a CMR with and without inert particles inﬂuence signiﬁcantly the reactor performance for ﬁxed operating conditions (Georgieva-Angelova, 2008).

91

4 Transport Phenomena in Porous Membranes and Membrane Reactors

92

(a)

CMR

(b)

PBMR 15

axial velocity [–]

axial velocity [–]

20 15

10

10

5

5

lc axia

2

0

0.5

0.4

0.2

0.3

0.4

0.2

0.3

0

0.1

radial coordinate [–]

0.1

0.2

0.4

0.3

0.5

0

0.1

0.2

0.3

0.4

0.5

radial coordinate [–]

axia

radial coordinate [–]

4

]

(f)

1.5

4

0.15

0.1

0.05

radial coordinate [–]

0 0

axi al c

0.2

oor

2 0 0.25

din

ate

0.5

[–]

1

referred axial velocity [–]

(e)

4

te [–

2

l co

0

0

–0.3

ordi

2

–0.2 –0.25

axial

–0.3

nate

0

–0.1 –0.15

dina

[–]

–0.2

0 –0.05

coor

–0.1

radial velocity [–]

(d)

0

radial velocity [–]

0.5

–]

–]

radial coordinate [–]

(c)

referred axial velocity [–]

2

0

0

0.1

0 4

e[ inat oord

e[ inat oord

lc axia

0 4

1.5

1

0.5

0

4

0.2

oor ial c

0 0

radial coordinate [–]

–]

te [ dina

2

0.1

ax

Figure 4.5 Velocity proﬁles in CMR with and without packed bed for GHSV = 27 736 L/h, SS/TS = 9, T = 600 °C.

4.3 Velocity Fields in Membrane Reactors

1.5

v max v

[-]

2

1 SS/TS=9 SS/TS=0.4

0.5 0

1

2

3

4

axial coordinate [-] Figure 4.6

Development of the scaled maximal velocity.

For PBRs the velocity ﬁelds have been computed using the Brinkman– Forchheimer equation: −∇⋅

(ε

Re

)

∇v − ε v ⊗ v + ε∇p + σ ( v ) = 0,

∇⋅ (ε v ) = 0,

(4.4)

where ε = ε(r) denotes the radial symmetric porosity, Re is the Reynolds number and σ is a friction force. The existence and uniqueness of a weak solution for a linear friction term σ ( v ) = σ v under appropriate boundary conditions has been shown by (Skrzypacz and Tobiska, 2005). In the simplest case of a plane channel of gap L with a constant porosity ε(r) = ε = const, the analytical solution: cosh λ ( y − L 2) ⎞ ⎞ ⎛ p1 ⎛ 2 v = ⎜ ⎜1 − ⎟ , 0⎟ , p = p0 − p1x , λ = σ Re ε ⎝σ ⎝ cosh λL 2 ⎠ ⎠

(4.5)

for the fully developed ﬂow can be used to evaluate the accuracy of different numerical solutions. We found that the Q 2 P1disc solution computed by the inhouse code MooNMD approximates the analytical solution already on a coarser mesh with the same accuracy as the P2/P1 solution computed by the COMSOL package (Chapter 2). In case that the porosity is not constant there is no longer an analytical expression for the fully developed velocity proﬁle available. Therefore, the proﬁles have been computed by MooNMD with the accurate Q 2 P1disc ﬁnite element for different Reynolds numbers. Figure 4.7 shows clearly the tunneling effect due to decreasing porosity in the neighborhood of the reactor wall. Although there is no exact representation of the developed proﬁle, the method of matched asymptotic expansions can be used to construct an analytical approximation in the case of a high Reynolds number. For this let the friction term be α v + β v v . Assuming a linear pressure drop p = p0 − p1z we get given by σ ( v ) = Re for the developed velocity proﬁle Φ = Φ(r) in a tube of radius R the two-point boundary value problem:

93

4 Transport Phenomena in Porous Membranes and Membrane Reactors 3

velocity magnitude [-]

94

Re=1 Re=500

Re=25

2

1

0 0,5

0,6

0,7

0,8

0,9

1

dimensionless radial coordinate [-] Figure 4.7

Fully developed velocity proﬁles in PBR for different Reynold numbers.

(

)

1 ⎡ 1 ∂ ∂Φ − rε (r ) + α (r ) Φ ⎤ + β (r ) Φ Φ = ε (r ) p1 , Φ ′ (0 ) = Φ (R ) = 0, ⎥⎦ ∂r Re ⎢⎣ r ∂r (4.6)

which can be solved by a ﬁnite element method on layer-adapted grids (Roos, Stynes, and Tobiska, 2008) or for high Reynolds numbers by the matched asymptotic expansion method (Goering, 1977). The asymptotic expansion up to ﬁrstorder terms is: Φ as ( r ) =

p1ε ( r ) pε − 1 R β (r ) βR

3 ⎛ (R − r ) Re cosh ⎜ 2 ⎝ 2

4

p1 βR ⎞ +γ ⎟ εR ⎠

, 3 cosh h2 ( γ ) = 1, γ > 0.

(4.7)

In Figure 4.8 we compare the ﬁrst order asymptotic approximation for Re = 1000 with the 1-D ﬁnite element solution which are in good agreement. Note that the asymptotic approximation is valid for the limit case Re → ∞ and therefore valid only for high Reynolds numbers. The 1-D ﬁnite element approximation can be used for the full range of Reynolds numbers as a method to avoid 2-D and 3-D computations whenever only developed proﬁles are of interest. Figure 4.9 presents the velocity proﬁles for a PBMR with a uniform dosing proﬁle over the reactor length. We see that, with an appropriate scaling, one uses the concept of selfsimilar solutions also in this case. Concerning an accurate numerical computation of velocity ﬁelds, particularly for PBMR with large velocity gradient near the wall, we performed several tests which show that the quality of the ﬁnite element solution of the incompressible Navier–Stokes equation strongly depends on the pair of ﬁnite elements used to discretize velocity and pressure. In particular, the local mass conservation – important when coupled ﬂuid-transport phenomena are computed – is much better satisﬁed for discontinuous pressure approximations than for continous ones (Matthies

4.3 Velocity Fields in Membrane Reactors

velocity magnitude [-]

4 matched asymptotic 1d FE solution

3

2

1

0 0.5

0.6

0.7

0.8

0.9

1

dimensionless vertical direction [-] Figure 4.8

Developed velocity proﬁles for the PBR for Re = 1000.

Figure 4.9

Self-similar velocity proﬁles in PBMR for Re = 50.

and Tobiska, 2007). Therefore, instead of using continuous, piecewise polynomials of degree k ≥ 2 to approximate the velocity on triangular or tetrahedral meshes and continuous, piecewise polynomials of degree k − 1 for the pressure (Taylor– Hood element), we propose to approximate the pressure by piecewise, discontinuous polynomials of degree k − 1. However, combined with a continuous, piecewise polynomial approximation of degree k on triangular and tetrahedral meshes this would lead to an unstable ﬁnite element pair which does not satisfy the inf-sup stability condition already mentioned in Chapter 2. In order to fulﬁll the stability condition the velocity space can be enriched by additional bubble functions or the discontinuous pressure space can be used with a velocity space of continuous,

95

96

4 Transport Phenomena in Porous Membranes and Membrane Reactors

Figure 4.10 Errors of the (Q 2 , P1disc ) solution (diamonds), the (Q 3 , P2disc ) solution (stars) and the post-processed solution (circles).

piecewise polynomials of degree k in each variable on quadrilateral and hexahedral meshes, respectively (Girault and Raviart, 1986). We denote this inf-sup stable element pair brieﬂy by (Q k , Pkdisc −1 ). Numerical experiments verify the theoretically predicted convergence rates of order k with respect to the (H1,L2) – norm. Moreover, (Matthies, Skrzypacz, and Tobiska, 2005) proved that, for k = 2, a special interpolant is superclose; more precisely the error of the computed discrete solution to the interpolated analytical solution is one order better than it is to the analytical solution. Based on this theoretical result a local postprocessing applied to the computed discrete solution leads to a discrete solution with enhanced accuracy. Figure 4.10 shows the convergence rates of the errors of the computed discrete solutions for the 3-D test example on the unit cube Ω = (0,1)3with the analytical solution: ⎧ ⎫ ⎪ ⎪ sin (π x ) sin (π y ) sin (π z ) + x 4 cos (π y ) ⎪ ⎪ u=⎨ cos (π x ) cos (π y ) cos (π z ) − 3y 3z ⎬ ⎪ 9 2 2⎪ 3 ⎪cos (π x ) sin (π y ) cos (π z ) + cos (π x ) sin (π y ) sin (π z ) − 4 x z cos (π y ) + y z ⎪ ⎩ ⎭ 2 p = 3x − sin ( y + 4 z ) − p0 (4.8)

and the Reynold number Re = 10. For a given mesh the next ﬁner mesh is constructed by dividing each cube into eight subcubes such that the ﬁnest mesh corresponds to 6 440 067 velocity and 1 048 576 pressure degrees of freedom for the (Q 2 , P1disc ) discretization (Figure 4.10, diamonds). Note that the higher order element (Q 3 , P2disc ) (Figure 4.10, stars) is more accurate already on a coarser mesh level with

4.4 Determination of Transport Coefﬁcients and Validation of Models

352 947 velocity and 40 960 pressure degrees of freedom. We see that the accuracy of the (Q 2 , P1disc ) solution on the ﬁnest mesh is almost achieved by the post-processed (Q 2 , P1disc ) solution on a mesh with only 107 811 velocity and 16 384 pressure degrees of freedom. The gain in accuracy by post-processing increases due to the different convergence rates O(h2) and O(h3), respectively. Thus, the computational effort for a certain accuracy can be drastically reduced, in particular if local postprocessing is used only in regions of interest. For more details we refer to (Matthies, Skrzypacz, and Tobiska, 2007). It is important to note that the mixed ﬁnite element discretizations of the Stokes, Navier–Stokes and the extended Brinkmann equation lead to a nonlinear algebraic system of a saddle point type for which sophisticated algorithms have been developed (Turek, 1999; John et al., 2002).

4.4 Determination of Transport Coefﬁcients and Validation of Models

In the following we discuss mass transport in ceramic membranes based on results by (Hussain, Seidel-Morgenstern, and Tsotsas, 2006) and (Thomas, 2003) and mass transport in sinked metall membranes based on results by (Edreva et al., 2009). Both types of membranes are porous and asymmetric. They differ not only in material and structure, but also in the fact that all precursors were available for the ceramic membranes, whereas just the ﬁnal composite was available in the case of metallic membranes. This leads to different methodologies of parameter identiﬁcation and validation in Sections 4.4.1 and 4.4.2. Section 4.4.3 shows that the quality of prediction of some mass transfer experiments can be further increased by the use of 2-D CFD models. This section is based on results summarized by (Georgieva-Angelova, 2008). The identiﬁcation of thermal parameters of the membranes and the prediction of the results of experiments with combined mass and heat transfer are not discussed here with reference to work by (Hussain, Seidel-Morgenstern, and Tsotsas, 2006). 4.4.1 Mass Transport Parameters of Multilayer Ceramic Membranes – Precursors Available 4.4.1.1 Task and Tools The dusty gas model (DGM) presented in Chapter 2 can be used (despite the already-mentioned criticism) to describe mass transport in porous membranes. As already discussed (see Equations 2.49 to 2.54), the model has three parameters (B0, K0, F0) that quantify viscous ﬂow, Knudsen diffusion and molecular diffusion, respectively, in a porous membrane. To translate this formal quantiﬁcation into morphological features of the membrane, additional assumptions are necessary. Here we assume tortuous, monodispersed capillaries, which are neither interconnected, nor change their cross-sectional area with their length. Then, the three parameters of the DGM can be expressed as:

97

98

4 Transport Phenomena in Porous Membranes and Membrane Reactors

B0 = F0

2 d pore 32

(4.9)

K 0 = F0

d pore 4

(4.10)

F0 =

ε τ

(4.11)

As Equations 4.9 to 4.11 reveal, in the frame of the selected simple model for membrane structure only two of the three parameters are independent from each other. K0 and B0 are selected as those two parameters. They correlate with the diameter of the assumed capillaries: d pore =

8B0 K0

(4.12)

and with the ratio ε/τ :

ε (K 0 )2 = 2B0 τ

(4.13)

between the porosity ε and tortuosity τ of the membrane. Consequently, in order to describe mass transport with the DGM, the parameters K0 and B0 (or dpore and ε/τ ) must be identiﬁed with the help of experimental results. For a multilayer membrane, this identiﬁcation should be done for every single layer. In the present section we refer to tubular multilayer ceramic membranes with available precursors. Such membranes consist of one support layer (α-Al2O3), two or three intermediate layers (also α-Al2O3) and one separation layer (γ-Al2O3). Availability of precursors means that – in the case of two intermediate layers – we have the support membrane, the membrane consisting of the support and the ﬁrst intermediate layer, the membrane consisting of support and two intermediates and, ﬁnally, the complete multilayer membrane. This was possible by close cooperation with the producer of the ceramic membranes (Inocermic GmbH, Hermsdorf, Germany). Identiﬁcation of the mass transport parameters is carried out by means of single gas permeation experiments. The validity of parameters gained in this way is checked by additional experiments of isobaric diffusion and transient diffusion. The principles of all three mentioned isothermal experiments are summarized in Figure 4.11 and Table 4.1, where the index “o” is used for the shell-side (annulus) and the index “i” for the tube-side of the reactor. More explanations are given in subsequent sections. All measurements can be conducted in the experimental set-up illustrated in Figure 4.12, which is an extended Wicke–Kallenbach cell for tubular specimens. Various valves and mass ﬂow controllers (MFC) enable accurate dosing of gases at the tube and/or shell side of the membrane in the measuring cell. At both outlets the gas composition and gas ﬂow rates can be measured by a thermal conductivity GC sensor and various instruments (depending on the absolute value

4.4 Determination of Transport Coefﬁcients and Validation of Models (a)

(b)

(c)

Figure 4.11 Principles of isothermal experiments used in order to identify and validate the mass transport parameters of porous membranes.

Table 4.1

Main features of the experiments from Figure 4.1.

Experiment

Conditions

Components

Principal measured quantity

Purpose

Single gas permeation

Steady state

Pure gas

po − pi

Identiﬁcation of K0, B0

Isobaric diffusion

Steady state

Two components

yj,o,out, ug,o,out1 yj,i,out, ug,i,out

Validation

Transient diffusion

Transient

Two components

po(t) − pi

Validation

99

100

4 Transport Phenomena in Porous Membranes and Membrane Reactors

Figure 4.12

Schematic of experimental set-up.

of the gas ﬂow rate), respectively. Additionally the pressure difference between tube and annulus and several absolute pressures are determined. If necessary, isobaric conditions can be attained by a ﬁne adjustment of the needle valves at both gas outlets. Several methods of sealing have been tried out, including conventional O-rings and slightly conical graphite rings. The tightness between the tube- and shell-side of the membrane as well as tightness to the environment have been checked by a helium leakage detector and by pressure measurements. The reactor is placed in a controllable oven, so that different temperature levels can be set for isothermal experiments. An electrical heater that can be placed in the tube, gas pre-heaters, post-coolers, insulations and various measurements of temperature enable additional, non-isothermal modes of operation. 4.4.1.2 Identiﬁcation by Single Gas Permeation In the single gas permeation experiment according to Figure 4.11a a pure gas is introduced at the shell-side, is pressed through the membrane and leaves the cell at the end of the tube. Under such conditions, the general DGM equation for a homogeneous membrane (2.60) reduces to:

n j = −

B 1 ⎛4 8RT + 0 K0 ⎜ πM j η j RT ⎝ 3

⎞ p ⎟ ∇p ⎠

(4.14)

4.4 Determination of Transport Coefﬁcients and Validation of Models

For cylindrical coordinates and a relatively moderate membrane thickness, integration of Equation 4.14 leads to the expression: ⎛4 N j B 2π L 8RT =− K0 + 0 ⎜ r Δp ⎛ π ηj M ⎞ 3 j ln ⎜ m ,o ⎟ ⎝ RT ⎝ rm ,i ⎠

⎞ p⎟ ⎠

(4.15)

Equation 4.15 means that the permeate ﬂux of the membrane (the ratio N˙j/Δp) should be a linear function of the average pressure in the membrane (¯p = (po + pi)/2). Consequently, linear regression of respective experimental data gives the Knudsen coefﬁcient K0 from the intercept and the permeability constant B0 from the slope of the resulting straight line. The measurements necessary in every single permeation experiment are those of pressure drop, Δp = po − pi, one absolute pressure (po or pi) and gas molar ﬂow rate, N˙j. After K0 and B0 of the support layer of a composite membrane have been determined in this way, single gas permeation experiments are conducted with the composite precursor consisting of the support and the ﬁrst intermediate layer. Application of Equation 4.15 to the support with the previously determined values of K0 and B0 delivers the pressure at the interface between support and intermediate. In this manner, pressures and ﬂuxes are known for the intermediate layer, so that K0 and B0 can be derived also for this layer. Recursively, the mass transport parameters of every layer of any composite membrane are obtained, provided that all precursors of the composite are available. Results of the application of this scheme to three ceramic membranes, one with a large diameter (membrane 1) and two with a small diameter (membranes 2a and 2b) are presented in Table 4.2. Herein, layer thicknesses have been taken over from producer information. Comparison between membranes 2a and 2b shows that the structural properties of membranes, which are nominally the same but belong to different production charges, may differ to a certain extent. Defects or ﬁssures have an even stronger inﬂuence on membrane properties. It is obvious from the foregoing discussion, that a certain variation of the pressure level is necessary in order to obtain mass transport parameters from single gas permeation experiments. This variation is in the range of 1–3 bar (1 bar = 100 kPa) in the present work. Variation of temperature or of the used gas is strictly not necessary. However, it can serve as a check for the consistency of the derived values of K0 and B0 – which should not depend systematically on the temperature level or on the kind of the gas. For this reason, because temperature is an important operating parameter of membrane reactors, and because multicomponent gas mixtures appear in practice, an ample variation of temperature (20–500 °C) has been conducted for three different gases (air, N2, He). Representative experimental results for the large membrane (membrane 1, see Table 4.2) are shown and compared with calculations in Figures 4.13–4.16. First, single gas (N2) permeation data gained with the (homogeneous) support of this membrane at different temperatures are depicted in Figure 4.13, illustrating that the linearity foreseen by Equation 4.15 is fulﬁlled. According to the same

101

102

4 Transport Phenomena in Porous Membranes and Membrane Reactors

Table 4.2

Layer

Mass transport parameters of three ceramic membranes. Material

Thickness [μm]

K0 [m]

B0 [m2]

dpore [nm]

ε/τ

Membrane 1, L = 250 mm, rm,i = 10.5 mm, rm,o = 16 mm (approx.) according to Hussain, 2006 Support 5500 α-Al2O3 8.16 × 10−8 2.96 × 10−14 2900 25 First intermediate 7.99 × 10−8 2.73 × 10−14 2730 α-Al2O3 −9 25 76.5 Second intermediate 2.98 × 10 2.85 × 10−17 α-Al2O3 −9 2 29.4 Separation 2.03 × 10 7.47 × 10−18 γ-Al2O3

0.112 0.124 0.156 0.277

Membrane 2a, L = 200 mm, rm,i = 3.5 mm, rm,o = 5 mm (approx.) according to Hussain, 2006 Support 1500 α-Al2O3 8.80 × 10−8 3.32 × 10−14 3010 −8 25 First intermediate 7.95 × 10 2.56 × 10−14 2570 α-Al2O3 −9 25 284 Second intermediate 7.71 × 10 2.74 × 10−16 α-Al2O3 25 110 Third intermediate 5.72 × 10−9 7.88 × 10−17 α-Al2O3 2 4.94 Separation 8.83 × 10−11 5.45 × 10−20 γ-Al2O3

0.117 0.124 0.109 0.208 0.072

Membrane 2b, L = 300 mm, rm,i = 3.5 mm, rm,o = 5 mm (approx.) according to Thomas, 2003 Support 1500 α-Al2O3 9.34 × 10−8 3.58 × 10−14 3070 25 First intermediate 4.11 × 10−8 9.47 × 10−15 1840 α-Al2O3 −9 25 191 Second intermediate 9.40 × 10 2.24 × 10−16 α-Al2O3 −9 25 76 Third intermediate 5.97 × 10 5.69 × 10−17 α-Al2O3 2 16 Separation 1.11 × 10−9 2.18 × 10−18 γ-Al2O3

0.122 0.089 0.197 0.313 0.283

equation, the inﬂuence of temperature should be proportional to T−1/2 in the Knudsen regime and very strong – proportional to approximately T−1.75 – in the viscous regime. The latter is a combination of the explicit, inverse proportionality on temperature of Equation 4.15 with the temperature dependence of viscosity (ηj ∼ T 0.75 according to [Schlünder and Tsotsas, 1988]). As we see in Figure 4.13b,c, the intercepts and slopes of the straight lines of Figure 4.3a agree well with these theoretical expectations. However, the intercept (Knudsen diffusion) represents single gas permeation only at the limit of ¯p → 0, and the slope (viscous ﬂow) only at the limit of ¯p → ∞. In reality, we have a certain ﬁnite value of average pressure and, thus, a mix of Knudsen diffusion and viscous ﬂow that depends on the speciﬁc value of ¯p and on the structure of the membrane. Consequently, the temperature dependence is characterized by an exponent somewhere between −0.5 and −1.75. This is illustrated in Figure 4.14. For moderate pressures in the rather permeable support the ﬂow rate is approximately proportional to T −1 (Figure 4.14a). The ﬂow rate through the composite membrane is always signiﬁcantly lower than the ﬂow rate through the support, due to the mass transport resistance of the additional layers. Since these layers have smaller pores, the inﬂuence of Knudsen diffusion increases, which is reﬂected in a weaker dependence of the ﬂow rate upon temperature in the composite membrane. Results of N˙j/ΔP over pressure for every individual layer of membrane 1 are shown in Figure 4.15. We see small intercepts and large slopes for the support and the ﬁrst intermediate

4.4 Determination of Transport Coefﬁcients and Validation of Models (a)

(b)

(c)

Figure 4.13 a) Results of single gas (N2) permeation experiments for the support of membrane 1 at different temperatures. b) and c) Temperature dependence of the intercepts and slopes of the respective straight lines.

Figure 4.14 a) Logarithmic and b) linear plots for the inﬂuence of temperature on single gas permeation through the support and the composite membrane 1 at the lowest realized pressure level of approximately 1 bar.

103

104

4 Transport Phenomena in Porous Membranes and Membrane Reactors

Figure 4.15

(a)

Single gas permeation (N2, 25 °C) for every individual layer of membrane 1.

(b)

Figure 4.16 a) Results of permeation experiments with two different gases for the support of membrane 1 and for the composite membrane 1 at 25 °C. b) Dependence of the slopes of respective lines on gas molar mass.

layer, which means that viscous ﬂow dominates. In contrast, Knudsen diffusion dominates for the second intermediate and the separation layer, so that large intercepts and very small slopes are obtained. Evaluated pore diameters reﬂect this behavior (Table 4.2). As to the inﬂuence of the gas, it is clear that He permeates easier than air or N2 (Figure 4.14). This is veriﬁed by Figure 4.16, which also reveals some additional 2 −1 interesting features. Equation 4.15 suggests a dependence on M in the intercept j 6 −1 (Graham’s law). Dynamic gas viscosity is proportional to approximately M (see, j 1j 6. e.g., Schlünder and Tsotsas, 1988, p. 76), so that the slope should depend on M Figure 4.16b shows explicitly that the expectation concerning the inﬂuence of molar mass on the slope is fulﬁlled by data for the support. Graham’s law is also

4.4 Determination of Transport Coefﬁcients and Validation of Models

fulﬁlled by this data (open symbols), though not explicitly illustrated. The same is not true for data gained with the composite membrane 1 (full symbols). Speciﬁcally, the slope of single gas permeation data decreases with increasing molar mass for the composite, while it increases for the support (Figure 4.16b). This inversion in respect to the behavior of a homogeneous porous body is a result of complicated combination of several Knudsen and viscous contributions in the different layers. It can be used for diagnosis of composite membrane structure. Such diagnosis cannot be done on the basis of linearity in permeation plots, because plots of this kind (e.g., Figure 4.16a) are nearly linear for both homogeneous membranes and composites. The issue of diagnosis is important in connection with membranes of completely unknown structure and, thus, is further discussed in Section 4.4.2.1. 4.4.1.3 Validation by Isobaric Diffusion and by Transient Diffusion Though the single gas permeation experiment discussed in the previous section primarily serves the purpose of identifying the transport parameters of the membrane, it also has validation features given by variations in the temperature and the kind of gas used. Additional validation is possible by experiments using isobaric diffusion and transient diffusion. In isobaric diffusion according to the principle of Figure 4.11b, helium can be sent through the tube-side and nitrogen through the shell-side of the membrane. Helium is transported from the tube to the annulus by Knudsen and molecular diffusion, and viscous ﬂow does not take place because of equal pressure in the two compartments. Consequently, at the outlet we have some helium in the annulus (˜ y He,o,out > 0) and some nitrogen in the tube ( yN2 ,i ,out < 1). The values of ˜ y He,o,out and ˜ y He,i,out can be measured and also calculated quite accurately, as Figure 4.17a shows. The calculation is conducted by reducing the dusty gas model (2.60) for isobaric conditions to the relationship:

(a)

(b)

Figure 4.17 Measurement and prediction for isobaric diffusion through the composite membrane M1 (tube inlet: pure helium; annulus inlet: pure nitrogen): a) outlet molar fractions of helium, b) velocity at the outlet of the tube.

105

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4 Transport Phenomena in Porous Membranes and Membrane Reactors

yk n j − y j n k DK , j Δy j p + n j = − DK , j D jk RT r ln (rm ,o rm ,i ) ετ k =1, k ≠ j N

∑

(4.16)

with ¯r = (rm,o − rm,i)/2, and applying this equation to every layer of a composite membrane. Equation 4.16 is coupled to the mass balances for the two compartments of the cell (SS, TS), assuming that axial dispersion can be neglected and using appropriate mass transfer coefﬁcients (Hussain, Seidel-Morgenstern, and Tsotsas, 2006). Figure 4.17a shows that the difference between the outlet molar fractions of helium decreases with decreasing velocity of incoming helium – that means with increasing residence time of helium in the tube. Because of Knudsen diffusion in the membrane, mass transfer between the compartments is not equimolar, so that the outlet and inlet velocities are different from each other. Speciﬁcally, the tubeside outlet velocity, ug,i,out, will be smaller than the shell-side outlet velocity, ug,o,out, because Knudsen diffusion favors the transfer of helium (the smaller molecule) from the tube to the annulus. The respective measured results can also be predicted well, see Figure 4.17b. In the case of transient diffusion, the shell-side is kept closed and the cell is initially ﬁlled with nitrogen (gas “k”, see Figure 4.11c). Then (at t = 0), the tube ﬂow is switched to helium (gas “j”). Due to preferential diffusion of helium through the membrane the pressure increases in the closed shell-side (Figure 4.18). This trend is opposed by viscous ﬂow, so that an equilibration of pressure and an atmosphere of pure helium are obtained throughout the entire cell after some time. For calculation, the complete DGM must be used, because Knudsen diffusion, molecular diffusion and viscous ﬂow take place simultaneously. The tubeside mass balance is treated in the same way as for isobaric diffusion. Spatially concentrated conditions can be assumed in the shell-side, reducing the respective mass balance – after application of the ideal gas law – to:

Figure 4.18 Measurement and prediction for transient diffusion (see Figure 4.1c) through the composite membrane M1 and its support.

4.4 Determination of Transport Coefﬁcients and Validation of Models

m ,o dpo RTA = (n j ,m ,o + n k ,m ,o ) dt Vo

(4.17)

As Figures 4.15 and 4.16 show, the results of validation experiments can be satisfactorily predicted by the DGM using the previously identiﬁed parameters K0 and B0. The structural parameters dpore and ε/τ, which can be derived from K0 and B0, have values within reasonable ranges (Table 4.2) and show reasonable trends when going from the support to the selective layer of the composite membrane. However, it would be a mistake to consider dpore, ε and τ as the real values of average pore diameter, porosity and tortuosity in the porous media. The reason for this are the radical assumptions made in in order to connect K0 and B0 with dpore and ε/τ by Equations 4.12 and 4.13. Additionally, defects and inhomogeneities are present in real membranes, transitions from one layer to the other are not sharp and inaccuracies occur in measurement, identiﬁcation and determination of layer thicknesses. 4.4.2 Mass Transport Parameters of Metallic Membranes – Precursors not Available

Following the same procedure as in Section 4.4.1, our intention is to identify the DGM parameters of metallic membranes with the help of single gas permeation measurements and validate them by means of isobaric and transient diffusion experiments. The investigated tubular metallic membrane was produced by Fa. GKN Sinter Metal Filters GmbH. It has the same effective length as the ceramic membrane L = 120 mm and, with rm,i = 10.55 mm, it has approximately the same inner diameter; but it is thinner, with an outer radius of rm,o = 12.8 mm. No more information is available about this membrane. 4.4.2.1 Diagnosis Single-gas permeation experiments have been conducted with air, argon and helium for different temperatures (26–500 °C) and pressures (1.5–3.0 bar). Without any further information about the membrane structure, these experiments have been evaluated by assuming the membrane to be homogeneous. In this way, the Knudsen diffusion coefﬁcient, bulk ﬂow coefﬁcient, dpore and ε/τ given in the upper part of Table 4.3 have been calculated. Figure 4.19 shows permeate ﬂuxes of He at different temperatures (full symbols) plotted against the mean pressure. It is evident that the single-layer model can describe the results of single-gas permeation experiments with good accuracy. For validation, isobaric diffusion experiments have been carried out at a constant ﬂow velocity (ug,o,in = 0.043 m/s) of pure nitrogen at the inlet of the annulus and various ﬂow velocities of pure helium at the inlet of the tube. The respective experimental results are plotted in Figure 4.20. Again, we expect the difference between the outlet molar fractions of helium (˜ y He,i,out and ˜ y He,o,out) to increase with ug,i,in. However, the calculation conducted with

107

108

4 Transport Phenomena in Porous Membranes and Membrane Reactors Table 4.3 Mass transport parameters of metallic membrane with different methods of

identiﬁcation. Layer Membrane, L One layer Two layers First layer Second layer

Material

Thickness [μm]

K0 [m]

B0 [m2]

= 250 mm, rm,i = 10.55 mm, rm,o = 12.8 mm (approx.) Inconel 600 2250 1.48 × 10−7 3.10 × 10−14 Inconel 600 Inconel 600

1125 1125

1.21 × 10−7 1.06 × 10−7

1.69 × 10−14 1.39 × 10−13

dpore [nm]

ε/τ

1 677

0.353

1 119 10 490

0.432 0.040

Figure 4.19 Results of single gas (He) permeation experiments for the metallic membrane at different temperatures and calculations based on the single-layer model. Full symbols: ﬂow from SS to TS; empty symbols: inversed ﬂow (Edreva et al., 2009).

Figure 4.20 Measurement and calculation for isobaric diffusion (tube inlet: pure helium; annulus inlet: pure nitrogen) based on the assumption of a spatially homogeneous membrane with parameters gained from single gas permeation.

4.4 Determination of Transport Coefﬁcients and Validation of Models

Figure 4.21

Measurement and calculations for transient diffusion.

the B0 and K0 from the upper part of Table 4.3 predicts conditions close to equilibrium at the outlet of the membrane, in contrast to the measurements. This means that Knudsen diffusion and molecular diffusion are signiﬁcantly overestimated in the calculation. Transient diffusion experiments have been conducted by using two gases, N2 and He, with a signiﬁcant difference in their molar masses. The comparison between experiment and simulations with the single-layer model in Figure 4.21 also shows an overestimation of the diffusion of helium from the tube to the closed annulus compartment, which leads to an overestimation of the maximum of shellside pressure by the model (dashed curve). The foregoing analysis shows that different modes of mass transport cannot be properly described when assuming a homogeneous membrane. This is a strong indication of a multilayer membrane structure, posing the question about additional methods for the non-destructive diagnosis of such structures. It is known from the literature that the permeate ﬂux of asymmetric membranes may depend on the direction of ﬂow (Uchytil, Schramm, and Seidel-Morgenstern, 2000). For this reason, the direction of ﬂow, which had originally been from shell-side to tube-side, was inverted. However, the respective results, which are represented by empty symbols in Figure 4.19, do not differ signiﬁcantly from the previous results (full symbols). Therefore, ﬂow inversion is not an adequate method for the diagnosis of the multilayer structure of the present membrane. Another effect of structural inhomogeneity discussed in Section 4.4.1.2 refers to the inﬂuence of gas molar mass on the slope of permeate ﬂux lines. This effect does occur with our present metallic membrane. As Figure 4.22 shows, the slope of the permeance line decreases by transition from helium to argon, instead of increasing. The diagnosis of multilayer structure based on the failure of one-layer DGM to predict different mass transport experiments and the inversion of the molar mass effect was veriﬁed by breaking the metallic membrane. This revealed two layers

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4 Transport Phenomena in Porous Membranes and Membrane Reactors (a)

(b)

Figure 4.22 a) Results of permeation experiments with two different gases for the metallic membrane at 26 °C. b) Dependence of the slopes of respective lines on gas molar mass in double-logarithmic representation.

Figure 4.23

Sectional view for model of double layer membrane.

with approximately equal thickness. At the same time, it posed the problem of identifying B0 and K0 individually for each of the two layers of the membrane, when the precursors are not available. A solution to this problem is discussed in the following section. 4.4.2.2 Identiﬁcation In the next step, the same set of permeation experimental data with the metallic membrane is used to identify the parameters of a new two-layer model. These two layers (layer 1 and layer 2, with the same thickness) are shown schematically in Figure 4.23. For modeling single-gas permeation through a multilayer membrane, Equation 4.15 can be written in the form:

4.4 Determination of Transport Coefﬁcients and Validation of Models

⎞ ⎛4 N j 2π L 8RT B =− K 0,i + 0,i p ⎜ j η j i ⎟⎠ r Δpi ⎛ 3 π M ⎞ ⎝ , + 1 m i ln ⎜ RT ⎝ rm ,i ⎟⎠

(4.18)

where: n

∑ Δp i =1

pi =

= pi − po

(4.19)

pint,i + pint,i +1 2

(4.20)

i

for i = 1, 2, …, n and: pint,1 = pi

(4.21)

pint,n +1 = po

(4.22)

Here n is the number of layers, and pint,i is the pressure between two membrane layers. For each set of pi and po a molar ﬂow rate N˙calc,j can be calculated by solving the group of equations and compared with the measured value N˙j. The parameter identiﬁcation problem is to ﬁnd the best set of parameters of B0,i and K0,i which minimize the differences of model prediction and real observation by minimizing the objective function: m

nj

J = ∑ ∑ w jk (N j ,k − N calc, j ,k )

2

(4.23)

j =1 k =1

Here, wij is a weighting factor, set to unity in the present work. To solve this optimization problem (see [Zhang, 2008] for more details) a genetic algorithm (GA) detecting the global optimum was used. After that, a local deterministic optimizer (LD) was applied to increase the accuracy of optimization. The combination of GA optimizer (Krasnyk et al., 2006) and LD optimizer (Rodriguez-Fernandez, Mendes, and Banga, 2006) is called a hybrid optimizer (Byrd et al., 1995). Both optimizers were incorporated in the DIANA simulation system (Teplinskiy, Trubarov, and Svjatnyj, 2005). The results of this derivation for the investigated membrane are summarized in the lower part of Table 4.3. The identiﬁed transport parameters imply one loose layer with relatively small pores and a second, highly compacted layer with a few large pores. As Figures 4.24 and 4.25 show, the agreement between calculations with the two-layer model and measurements is, again, very good. 4.4.2.3 Validation In Section 4.4.2.1 we discussed the single-layer model. The identiﬁed transport parameters of this model are capable of describing the results of single-gas permeation measurements even for a membrane that consists of two layers with signiﬁcantly different structures. The deﬁciencies of the single-layer model are not visible without a broad variation of operating parameters, and even with such a

111

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4 Transport Phenomena in Porous Membranes and Membrane Reactors

Figure 4.24 Results of single gas (He) permeation experiments (ﬂow from SS to TS) for the metallic membrane at different temperatures and calculations based on the two-layer model.

Figure 4.25 Results of single gas permeation experiments for three different gases at 1.5 bar (ﬂow from SS to TS) for the metallic membrane and calculations based on the two-layer model.

broad variation they do not jeopardize the good overall agreement between simulation and permeation data. Therefore, the supremacy of the two-layer model from Section 4.4.2.2 can hardly be demonstrated statistically on measured permeation data. Hence, the superiority of a model that realistically reﬂects the composite nature of the membrane (in our case of the two-layer model) becomes striking only when trying to validate the identiﬁed transport parameters with additional mass transfer experiments of another measuring principle, such as isobaric diffusion or transient diffusion.

4.4 Determination of Transport Coefﬁcients and Validation of Models

Figure 4.26 model.

Measurement for isobaric diffusion and prediction by means of a two-layer

Results for isobaric diffusion are presented in Figure 4.26. We can see that the two-layer model enables a satisfactory prediction of helium molar fractions measured in the shell-side and in the tube-side at the outlet of the cell. The simulation is carried without any change of the previously identiﬁed mass transport parameters (lower part of Table 4.3) and contrasts radically the spectacular collapse of the one-layer model when compared with the same data (Figure 4.20). Figure 4.26b shows that the gas ﬂow rate decreases in the tube along the membrane and gas velocities can also be predicted with satisfactory accuracy by means of the two-layer model. This results from preferential Knudsen diffusion of the smaller molecule (helium) from TS to SS and would not happen in the case of ordinary binary diffusion alone. The same is true for the transient diffusion experiment. The simulation results for the two-layer model are plotted by the solid line in Figure 4.21 and agree very well with the measured data, whereas calculation by the one-layer model (dashed line) does not describe the data well. Since the one-layer model does not properly describe different types of mass transfer measurements, it is necessary to use multilayer models for multilayer membranes in membrane reactor simulations, based on careful diagnosis, parameter identiﬁcation and validation. Finally, it is interesting to compare the ceramic and metallic porous membranes investigated in the present work. The comparison of single-gas permeation data reveals a helium permeation of about 0.9 × 10−6 mol/(s Pa) at 2 bar and ambient temperature for the metallic membrane (Figure 4.24) in contrast to about 0.18 × 10−6 mol/(s Pa) at similar conditions for the ceramic membrane. A comparison of the isobaric diffusion (Figures 4.17 and 4.26) and transient diffusion (Figures 4.18 and 4.21) shows that equilibration is faster with the metallic than with the ceramic membrane. Consequently, the thinner metallic membrane is characterized by higher permeability at comparable or even better selectivity. The metallic membranes are mechanically and thermally more stable. They would not easily get damaged by the relatively fast temperature changes occurring during start-up and shut-down

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4 Transport Phenomena in Porous Membranes and Membrane Reactors

of membrane reactors. Additionally, they can be more easily mounted and sealed, which facilitates membrane reactor design. In general, metallic membranes appear to be an attractive alternative to ceramics for membrane reactors. 4.4.3 Mass Transport in 2-D Models

Model descriptions with different complexity have been already presented in Chapter 2. The morphological parameters determined experimentally with the aid of the DGM are used for the 2-D simulations with FLUENT, after appropriate transformation. Validation can be conducted with the previously discussed steadystate experiments of single-gas permeation and isobaric diffusion. The consideration of transport phenomena such as diffusion and viscous slip in the membrane is particularly important in the 2-D CFD model. In case of a single-component ﬂow, the non-slip boundary condition on the walls can be used reliably. In binary or multi-component mixtures, especially in capillary ﬂows, this assumption is incorrect and may generate serious errors if the convective contributions are small and there is a large disparity in the molar masses of gas components (Young and Todd, 2005). It was derived by Kramers and Kistemaker (1943) that, in the presence of a concentration gradient parallel to the wall, the mixture would ﬂow along the wall with non-zero mass average velocity. They called this phenomenon diffusion slip. Viscous slip occurs in tube ﬂows when the molecular mean free path is a signiﬁcant fraction of the tube radius (Young and Todd, 2005). In multi-component tube ﬂow diffusion slip is important at all Knudsen numbers and exists even when the streamwise pressure gradient is zero (Young and Todd, 2005). In contrast, viscous slip is important in the Knudsen and transition regions. By means of algebraic transformations of the analytical solution for single-gas permeation, the parameters of the DGM can be converted to a form appropriate for usage in CFD simulations, whereas the viscous slip phenomenon is taken into account on the basis of integral quantities. The deﬁnition of the viscous resistance factor f1 has already been given in Equation 2.62. A comparison between experimental, analytical and numerical results is presented in Figure 4.27a for permeation of oxygen through the ceramic membrane 2a (see Table 4.2). A very good agreement for the permeation ﬂux N˙/Δp can be observed between the analytical and numerical results with a maximal relative error of 0.08%. With increasing temperature and pressure the deviation between experimental and calculated values rises maximally to 10%. Furthermore, the case of isobaric counter-diffusion of He versus N2 is used with parameters of membrane 1 (Table 4.2) for the comparison of results. Because both components have very different molar masses, the diffusion slip cannot be omitted. Considering the velocity resulting from the diffusion process via a source term in the momentum transport equations, excellent agreement with the experimental data can be achieved, Figure 4.27b. The use of such a source term leads to a pressure drop through the membrane of just a few pascals. Despite its small value,

4.5 Analysis of Convective and Diffusive Transport Phenomena in a CMR (a)

Figure 4.27

(b)

Validation of the 2-D model by transmembrane mass transport data.

this pressure difference is a key factor for obtaining close agreement between simulations and experiments. In the case of a dead-end reactor conﬁguration, where the mass ﬂow rate dosed at the shell inlet passes through the membrane, this pressure difference is negligible in comparison with the pressure drop related to convective ﬂow. Therefore, only the viscous slip on the pore walls is taken into account in this kind of simulation.

4.5 Analysis of Convective and Diffusive Transport Phenomena in a CMR

This study aims at providing a better understanding of the subprocesses, especially the transport phenomena in the membrane zones. In the catalytic membrane reactor with dosing strategy, the diffusion process of C2H6, fed at the tube inlet, to the shell side of the membrane has an important inﬂuence on the reactor performance. The loss of ethane or products at the interface between membrane support and the shell side is known from literature as a back-diffusion phenomenon. In the PBMR, the back-diffusion of reactants has an undesirable effect to bypass the catalytic bed and leads to a reduction in the conversion of reactants and yield of the product. In the CMR, the diffusion problem of reactants and products is more complicated. Two contradictory requirements can be formulated: (a) enough diffusion rates of ethane in radial direction as well as in the membrane catalytic layer are needed and (b) further diffusion to the annulus is undesirable. Therefore, an optimization-based design for the CMR is required to obtain the best reaction conditions. At ﬁrst, the concentration proﬁles for reactants and products are presented in Figure 4.28 for both CMRs with and without a packed bed. These results are related to the velocity ﬁelds already presented in the previous section.

115

4 Transport Phenomena in Porous Membranes and Membrane Reactors x 10-3 0.3094 0.6189 1.2379 1.8568 3.5838 0.3094, bed 0.6189, bed 1.2379, bed 1.8568, bed 3.5838, bed

6 5 4 3 2

4

0.3094 0.6189 1.2379 1.8568 3.5838 0.3094, bed 0.6189, bed 1.2379, bed 1.8568, bed 3.5838, bed

3 2 1

1 0

0

0.0

0.1

0.2

0.3

0.4

0.5

0.0

0.6

dimensionless radial coordinate [-] x 10-5 0.3094 0.6189 1.2379 1.8568 3.5838

4 3 2 1 0 0.0

0.1

0.2

0.3

0.4

0.5

dimensionless radial coordinate [-]

0.1

0.2

0.3

0.4

0.5

0.6

dimensionless radial coordinate [-]

mass fraction of ethylene [%]

5

x 10-3

mass fraction of oxygen [%] p

5

mass fraction of ethane [%] p

7

mass fraction of ethylene [%]

116

0.6

5

x 10-5 0.3094, bed

4

0.6189, bed 1.2379, bed

3

1.8568, bed 3.5838, bed

2 1 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

dimensionless radial coordinate [-]

Figure 4.28 Mass fraction proﬁles for reactor (CMR) with and without packed bed at different axial positions z/D for GHSV = 27 736 L/h, SS/TS = 9, T = 600 °C.

The mass fraction of ethane decreases in the tube side due to the reactions and system dilution caused by the dosed mass ﬂow rate. It increases continuously in the shell side, depending on the mass ﬂow rate at the tube inlet, membrane thickness and parameters as well as the total ﬂow rate in the reactor. In contrast, the mass fraction of oxygen rises permanently in the tube and decreases in the shell. Because the reactions take place in the membrane catalyst layer and ethane is transported only by diffusion, pronounced proﬁles are formed especially in the ﬁrst part of the reactor with and without a bed. For the CMR with an inert bed, the dispersion coefﬁcients are calculated as a function of the axial velocity and porosity proﬁles. Therefore, almost ﬂat proﬁles are developed near the reactor end with increasing the axial velocity in the tube. Ethylene is intensively generated near the inlet of both reactors and its mass fraction decreases with the length as a result of the consecutive reactions. Therefore, a change in the slope of the ethylene proﬁle can be observed. Near the inlets, ethylene is transported from the catalyst layer by diffusion and convection. Because of the increased mass fraction of ethylene in the reactor tube, its transfer from catalyst layer is only due to convection. Comparing the proﬁles in both reactors, it can be seen that more ethylene is produced in the reactor with a packed bed because of the better radial mass transfer.

4.5 Analysis of Convective and Diffusive Transport Phenomena in a CMR -6

x 10

tot

ethane mass flux [kg/(m²s)] p

4

m·

diffusion convection total

3

catalyst layer

2 1

m· C2 H 6 = m· tot y C H + m· CDiff 2H6 2 6

· y · Diff =–m tot C H + mC 2 H 6 2 6

0

-1 -2

0

0.01

0.02

0.03

0.04

0.05

0.06

axial coordinate [m]

Figure 4.29

Visualization of the diffusion-convection problem.

This result explains the advantage of the CMR with a packed bed, obtained on the basis of conversion of ethane, selectivity and yield of ethylene. The detailed consideration of diffusive species transport in the CMR is especially important for the understanding of the reactor behavior. Therefore, the diffusion-convection problem is discussed in the following. Locally considered, the mass balance for ethane at the interface between reactor tube and membrane can be expressed as in Figure 4.29. In order to have transport of ethane into the catalyst layer, the condition CDiff m 2H6 > m tot y C2H6 has to be fulﬁlled. This supposes that a maximal total ﬂux or a dosage limit exists, at which the amount transported by diffusion is still bigger than that transported by convection. At the value for which both amounts are equal, the mass ﬂux of ethane is zero and no more ethane can be transported into the catalyst layer. The local diffusion ﬂuxes can be quantiﬁed at the interfaces (not only for the catalyst layer but for all membrane layers) on the basis of Equation 4.24. The total ﬂuxes of ethane are given by Equation 4.25. CDiff m 2H6 = ρDC2H6 ,eff

∂y C2H6 r = Rm ∂r

(4.24)

C2H6 = ρDC2H6 ,eff m

∂y C2H6 + ρy C2H6 vr r = Rm ∂r

(4.25)

As an example, the diffusion ﬂuxes are calculated without reaction between the shell side and the membrane and are presented in Figure 4.29. Because the considered reactor has a dead-end conﬁguration, the entire amount of ethane has to be transported back to the tube side and the integral on the total ﬂux of ethane approaches zero with the accuracy of the numeric simulation. This is visualized on the basis of the ﬁlled areas under and over the curve of the total ﬂux. They are nearly equal, with an accuracy of ≈10−13. The diffusion ﬂux reduces with the length, because of a decreasing concentration gradient. In contrast, the magnitude of the convective ﬂux increases and the available amount of ethane in the shell side is transported again into the tube.

117

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4 Transport Phenomena in Porous Membranes and Membrane Reactors

Because in most of the simulations the SS/TS ratio is varied on the basis of an equal reactor residence time, the integral diffusion streams which are considered in the following are appropriately scaled to the mass ﬂow rate of ethane at the tube inlet. There are many possibilities to inﬂuence the back-diffusion phenomenon, from setting optimal operating conditions to choosing appropriate morphological membrane parameters. Therefore, the inﬂuence of some selected parameters is discussed in the following. The parameter ranges used are summarized in Table 4.4 (Section 4.6). At ﬁrst, the dependence of the diffusion ﬂuxes with variation of the volume ﬂow rate at the shell inlet is considered by keeping constant the tube inlet ﬂow rate and the results are presented in Figure 4.30. Varying the SS/TS ratio in this way corre-

Table 4.4 Inﬂuence parameters and their variation bounds.

Temperature, °C Total volume ﬂow rate, L/h SS/TS ratio: SS/TS = V˙SS/V˙TS Concentration ratio N = yC2H6 yO2 Tube diameter, mm Number of membrane layers Pore diameter in catalyst layer, nm Catalyst layer thickness, μm ε/τ ratio in the catalyst layer Pore diameter in support layer, nm Support thickness, mm ε/τ ratio in the support layer

480–620 15.0–68.36 0.4–9.0 2.0–3.5 1.75–5.0 Support, intermediate layers, separation layer 5–60 2–10 0.05–0.5 500–10 000 0.5–3.0 0.05–0.5

Figure 4.30 Inﬂuence of variation of the volume ﬂow rate at the shell side inlet on the diffusion rate at the interfaces tube-membrane and membrane-shell, T = 600 °C, without reaction.

4.5 Analysis of Convective and Diffusive Transport Phenomena in a CMR

sponds to different total volume ﬂow rates. The simulations are accomplished without consideration of the reactions and for three different constant ﬂow rates at the tube inlet. At the tube–membrane interface, Figure 4.30, a continuous increase of the diffusion stream and the scaled diffusion rate can be seen. By increasing the shell-side stream, the driving force for the diffusion process of ethane grows and the diffusion rate increases at this interface. In contrast, at the membrane-shell side, both diffusion ﬂux and ratio go through a maximum and, for higher shell-side volume ﬂow rates, the ethane loss through the membrane is suppressed despite the present diffusion driving force. For most of the simulations by parameter variation (see Section 4.6) the SS/TS ratio is changed on the basis of the same residence time. Some selected results for the inﬂuence of the morphological parameters as a function of SS/TS ratio on the diffusion rates at the membrane-shell side are presented in Figure 4.31. Among these parameters are the number of membrane layers, the support pore diameter, ε/τ ratio and thickness.

Figure 4.31 Inﬂuence of the number of membrane layers, the support pore diameter, ε/τ ratio and thickness on the diffusion ﬂuxes, GHSV = 6086 L/h, T = 600 °C.

119

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4 Transport Phenomena in Porous Membranes and Membrane Reactors

By increasing the SS/TS ratio, the inlet mass ﬂow rate of ethane becomes lower and the integral diffusion rate decreases signiﬁcantly. This tendency is different only for SS/TS = 0.4, whereas the tube-side stream is very high and the inﬂuence of external mass transfer resistances can be observed (see Section 4.6). Because of the longer residence time of the ethane molecules at higher SS/TS ratios (lower ﬂow rate at tube inlet), the scaled diffusion rate of ethane increases. By varying the number of the membrane layers at SS/TS = 9.0, 61–64% of the entered ethane mass ﬂow rate diffuses through the membrane. Under the given conditions, the number of layers has a very small inﬂuence on the diffusion rates. Taking the reactions into account, the diffusion rates of ethane are reduced in this case by about 10%. For the same total volume ﬂow rate, the inﬂuence of the morphological characteristics of the support is also studied with variations of the SS/TS ratio. It can be observed that the pore diameter of the support has only a minor inﬂuence on the reduction of the back-diffusion. A sixfold change in the pore diameter leads only to approximately 10% lower diffusion rates. This can be explained by the different dominant transport mechanisms. For higher pore diameters, the molecular diffusion and convective ﬂow are important for mass transfer process. The contribution of the molecular diffusion depends also on the ε/τ ratio. Therefore, the variation of the pore diameter inﬂuences the backdiffusion indirectly due to the formation of a larger pressure drop through the membrane. The inﬂuence of the pore diameter on the ethane diffusion is stronger in regions where Knudsen diffusion is the dominant mechanism, that is, in the catalyst layer. A very pronounced effect on the scaled diffusion rate of ethane is observed with variation of the ε/τ ratio and the support thickness, whereas the back-diffusion rates are reduced by more than 50% at SS/TS = 9.0. From the presented results can be concluded that the ethane and product loss through the membrane can be signiﬁcantly decreased with variation of the support thickness and ε/τ ratio, relatively independently from the catalyst properties. This gives the opportunity to choose them in an optimal way. Similar diffusion effects can be seen in the packed-bed membrane reactor, regarding the effect of the oxygen distribution. At low SS/TS ratios a limited distribution of oxygen is obtained (see Figure 5.11). The developing ﬂow behavior and the occurring reactions suppress the oxygen transport in the ﬁxed bed and lead to inefﬁcient use of the catalyst near the inlet. Therefore, the conditions for the reaction and the transport processes have to be adjusted to each other for an optimal operation of the reactor.

4.6 Parametric Study of a CMR

This section investigates the inﬂuence of various parameters on the CMR performance for oxidative dehydrogenation of ethane, using the 2-D mathematical model described in Chapter 2. The simulations serve as a basis for the analysis

4.6 Parametric Study of a CMR

and evaluation of the overall inﬂuence of the transport and reaction processes on the integral quantities like the conversion of ethane, selectivity and the yield of ethylene. The limits of variation in the reactor operating and geometrical conditions as well as the morphological membrane parameters are summarized in Table 4.4. The quantity Gas-Hourly-Space-Velocity (GHSV = V˙/Vm = 1/τ ) is deﬁned after (Ullmann, 1977) and is used by the following analysis. It is inversely proportional to the reactor residence time. Some of these parameters are interrelated and their correlations are given in Equations 4.26 and 4.27: Vtot = VSS + VTS ~ GHSV

(4.26)

SS VSS Vtot GHSV = = −1 = −1 VmVTS TS VTS VTS

(4.27)

The equations show that the volume ﬂow rate at the tube inlet depends on the total volume ﬂow rate and SS/TS ratio. The results from the simulation are presented here only for parameters with major inﬂuence. The effect of the other parameters, like the inﬂuence of the morphological parameters of the support, is discussed by Georgieva-Angelova, 2008. Before starting the simulation study, it is necessary to validate the model predictions not only for the transport processes, but also for the entire reactor performance. The comparison is carried out with experimental results for the CMR, provided by Klose et al. (Klose, 2008) and serves to validate the output of the simulation for the conversion of ethane, the selectivity of ethylene and the pressure drop. The comparison is accomplished for different SS/TS ratios, initial temperature and total volume ﬂuxes. A rather reliable prediction of the reactor tendencies can be obtained (see Figure 4.32). Because the conversions obtained by the experiments are always higher than the predicted ones, the catalytic layer thickness is varied between 2 and 3 μm. Better results are observed by using 3 μm catalyst layer thickness. No other parameters have been ﬁtted. In the simulations for parameter signiﬁcance, the morphological parameters after (Thomas, 2003) according to Table 4.2 are used. The usage of these parameters leads to better comparison results between simulation and experiment. At ﬁrst, comparisons between simulations with and without considering the energy balance are carried out in a wide range of parameter. Minimal differences of 0.05% under conditions of low conversion and 0.15% at higher conversion levels are obtained for the values of the ethylene yield, as shown in Figure 4.33. This indicates a pseudo-isothermal behavior. Nevertheless, most of the simulations are performed under consideration of the energy balance. A stronger inﬂuence of the temperature proﬁles in the reactor is expected when thicker catalytic layers with higher activity are applied and respectively higher conversions are achieved.

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4 Transport Phenomena in Porous Membranes and Membrane Reactors

selectivity of ethylene[%] p

conversion of ethane [%] p

122 8

2µm catlayst layer 3µm catalyst layer 6

experiment

4

2

0 450

490

530

570

610

100 80 60 40 2µm catlayst layer 3µm catalyst layer

20

experiment 0 450

650

490

530

T [°C]

610

650

x 104

8

8

2µm catlayst layer 3µm catalyst layer 6

6

experiment

Δp [Pa]

yield of ethylene [%] p

570

T [°C]

4

4 2µm catlayst layer 3µm catalyst layer

2

2

0 450

0 450

experiment

490

530

570

610

650

490

T [°C]

530

570

610

650

8

10

T [°C]

8

yield of ethylene [%] p

yield of ethylene [%] p

Figure 4.32 Comparison of results between experiment and numerical solution (GHSV = 27 737 L/h, SS/TS = 9, with inert bed).

isothermal non-isothermal 6

4

2

0 450

20 isothermal non-isothermal 15

10

5

0 490

530

570

T [°C]

610

650

0

2

4

6

SS/TS [-]

Figure 4.33 Inﬂuence on the ethylene yield at GHSV = 27 737 L/h, SS/TS = 9 and GHSV = 6086 L/h, T =620 °C.

4.6 Parametric Study of a CMR

4.6.1 Inﬂuence of Characteristic Geometrical Parameters

The transport resistances in the ﬂuid phase are often essential under laminar ﬂow conditions and can be a limiting factor for the entire reaction process. Under the given conditions in the CMR, the heat transfer limitations in the boundary layer are signiﬁcant in comparison with the thermal resistance of the membrane. Higher conversions and temperatures gradients in the reactor lead to a stronger inﬂuence on the external heat transfer resistances. Under the conditions of low reactant concentrations, a pseudo-isothermal reactor behavior is observed. Therefore, only the inﬂuence of the mass transfer resistances is studied in the following. The diffusion conditions for the reactants and products, for example for ethane, are inﬂuenced by varying the tube diameter. The external transport limitations can be estimated at identical gas dynamic conditions for all reactor geometries. The simulations are carried out with the boundary conditions of constant velocity at the tube inlet and constant SS/TS ratio. This means that the mass ﬂow rate at the inlet decreases respectively by lowering the tube diameter from 5.0 mm to 1.75 mm. The estimation of the external transport resistances is carried out after (Zanﬁr and Gavriilidis, 2003) and (Cussler, 1997) on the basis of a ratio between the times necessary for convective and diffusive transport. The convection time is given by Equation 4.28 and represents the required time of an element at position z to leave the reactor, that is, the “remaining residence time”. L−z v z ( z, r = 0 )

τk =

(4.28)

The diffusive time is deﬁned in Equation 4.29 as the time needed for a component to reach the wall of the catalytic layer from the reactor axis. The diffusion coefﬁcient is calculated according to Equation 2.46.

τd =

R2 Dij ( z )

(4.29)

Then, the following ratio F of the two times results in Equation 4.30: F=

Dij ( z ) L−z τk = τ d v z ( z, r = 0 ) R 2

(4.30)

When F > 1 or ln(F ) > 0, the molecules of ethane have enough time to reach the wall, because the time needed for the convective transport is higher than that for the diffusion process. When F < 1 or ln(F ) < 0, the molecules leave the reactor before reaching the catalyst layer. The simulations are accomplished for GHSV = 6086 L/h, SS/TS from 0.4 to 9.0 and the results are presented in Figure 4.34. The time available for the diffusion of ethane or F decreases signiﬁcantly with the reactor length. ln(F ) < 0 is observed for 55% of the reactor length for the tube radius Rt = 3.5 mm at SS/TS = 9.0. In

123

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4 Transport Phenomena in Porous Membranes and Membrane Reactors

(a)

(b)

Figure 4.34

Inﬂuence of the variation of the tube diameter for GHSV = 6086 L/h, T = 620°C.

comparison at SS/TS = 0.4, ln(F ) < 0 is obtained already at 14% of the reactor length. Clearly, the transport limitations of ethane in a radial direction have a signiﬁcant inﬂuence at lower SS/TS ratios. By increasing the tube radius, the diffusion limitations become more signiﬁcant. At Rt = 5.0 mm, SS/TS = 1.0 and SS/TS = 0.4, the ln(F) < 0 is observed for the whole reactor. When the tube radius is lowered to Rt = 1.75 mm, 77% of the length is free from diffusion limitations for all SS/TS ratios. This analysis does not consider the limitation of the ethane transport caused by the radial convective transport (discussed in Section 4.5). These results correspond to the obtained data for conversion of ethane and yield of ethylene. By lowering the tube radius, the conversion of ethane as well as the yield of ethylene increase rapidly. The usage of larger tube diameter leads to lower F ratios and accordingly to enhancement of the external mass transfer limitations. Therefore, the application of 2-D models is recommended for large-scale plants. 4.6.2 Inﬂuence of the Morphological Membrane Parameters in the Catalyst Layer

The inﬂuence of the pore diameter and the ε/τ ratio of the catalyst layer is investigated on the basis of modiﬁcation of the permeability constant and the Knudsen coefﬁcient according to Equation 2.51, and Equation 2.54. Their inﬂuence on the reaction distribution in the membrane catalyst and on the integral quantities is studied by keeping constant other structure parameters of the membrane. Furthermore, the effect of the catalyst layer thickness on the integral quantities is also of great interest.

4.6 Parametric Study of a CMR

Figure 4.35 Inﬂuence of the membrane parameters at GHSV = 27 737 L/h and 3 μm catalyst layer thickness.

An important aspect of the characterization of heterogeneous reactions is the estimation of effectiveness factor ηj, deﬁned in Equation 4.31 as a ratio of heterogeneous to homogeneous reaction rates.

ηj =

r j , heterogeneous ( yi ,ed , Tr ,z ) r j , homogeneous ( yi ,ed ,hom , Tr ,z )

(4.31)

The simulations are carried out at GHSV of 27 737 L/h, temperature of 873.15 K and operating pressure of 120 700 Pa with variation of the ratio SS/TS. Figures 4.35 and 4.36 present the results in terms of ethane conversion, ethylene selectivity and yield for 3 and 10 μm thicknesses, respectively. The latter value was found in the literature (Alfonso et al., 1999), for such catalytic layers. The effect of the pore diameter on the changes of the active surface is not considered. Therefore, the catalytic activity depends only on the layer thickness.

125

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4 Transport Phenomena in Porous Membranes and Membrane Reactors

Figure 4.36 Inﬂuence of the membrane parameters at GHSV = 27 737 L/h and 10 μm catalyst layer thickness.

The inﬂuence of the pore diameter on the ethane conversion is small at high ε/τ ratios for both membranes. Decreasing the pore diameter and ε/τ ratio at higher SS/TS ﬂow ratios leads to lower conversions and higher transmembrane pressure drop. In this case, the high resistance of porous medium limits the ethane diffusion in the catalyst layer. Consequently, the catalyst surface is not completely used. This effect is more pronounced for the 10 μm catalyst layer. The internal mass transfer limitations can be appropriate visualized on the basis of the effectiveness factor, for example, at ε/τ = 0.283 and SS/TS = 9 (Figure 4.37). The coordinates are dimensionless and are scaled to the reactor diameter. A good radial reaction distribution is obtained for 60, 16 and even for 5 nm pore diameters in the 3 μm layer. The effect of decreasing the pore diameter in the 10 μm layer leads to drastic reduction of the effectiveness factor up to 40% with the radial coordinate. Not only the conversion of ethane is negatively inﬂuenced, but also the selectivity to the intermediate products. Under the above conditions, the removal of ethylene from the reaction zone is limited and respectively lower ethylene selectivity is obtained in the reactor at small ε/τ ratios and pore diameters.

4.6 Parametric Study of a CMR (a)

(b)

Figure 4.37 Effectiveness factor for GHSV = 27 737 L/h, 3 μm and 10 μm catalyst layer, ε/τ = 0.283, SS/TS = 9.

Therefore, the lowest yield of ethylene at higher SS/TS ratios is observed at small ε/τ ratio and pore diameter because of the lowest selectivity and conversion. The inverse tendency for the conversion by variation of the pore diameter and ε/τ ratio is obtained at low SS/TS ratios for both membranes, except 10 μm, dpore = 5 nm und ε/τ = 0.05. A detailed discussion about this phenomenon is presented by (Georgieva-Angelova, 2008). When no internal transport limitations are observed in the catalyst layer, the maximal ethylene yield is limited by the active membrane surface area. For the example studied increasing the catalyst layer from 3 to 10 μm approximately triples the ethylene yield. The catalyst layer thickness has an essential impact on the reactor performance and manufacturing membranes with thicker catalyst layers will enhance the results for the conversion of ethane and the yield of ethylene, especially for higher GHSV values. 4.6.3 Inﬂuence of the Operating Conditions

This section investigates the inﬂuence of the averaged residence time in the reactor, the temperature, the ﬂow rate ratio SS/TS = V˙SS/V˙TS and the concentration ratio SS TS = VSS VTS in the ranges summarized in Table 4.4 and for a catalyst layer thickness of 3 μm. The graphics in Figure 4.38 show the inﬂuence of these parameters on the conversion of ethane, the selectivity and yield of ethylene and the transmembrane pressure drop. The following conclusions can be drawn:

•

Increasing the GHSV value (decreasing reactor residence time) leads to lower ethane conversions and ethylene yields. The variation of GHSV from 27 736 to

127

128

4 Transport Phenomena in Porous Membranes and Membrane Reactors

(a)

(b)

(c)

(d)

(e)

(f)

Figure 4.38 Inﬂuence of the operating conditions on the integral quantities, 3 μm catalyst layer, GHSV = 27 736 L/h.

4.6 Parametric Study of a CMR

Figure 4.39 Da number as a function of radial and axial coordinate at SS/TS = 9, T = 600 °C for both residence times.

6086 L/h results in >20% difference in the conversion of ethane. The selectivity values remain high with maximal 5.2% reduction at higher temperatures.

• •

The ethane conversions and ethylene yields rise signiﬁcantly with increasing the ﬂow rate ratio SS/TS in the considered range, especially at higher temperatures and higher residence times. The temperature has the largest inﬂuence on the ethane conversion among all investigated parameters with maximal difference of 25% in the observed range at GHSV = 6086 L/h.

The local reactant concentration determines the local reaction rates and thus determines the conversion and selectivity. Because the simulations are accomplished for low oxygen concentrations, higher selectivity of ethylene can be achieved by varying the others parameters. In contrast to PBMR no reaction limitation is observed in the catalyst layer under lean oxygen conditions even at SS/ TS = 0.4 and GHSV = 6086 L/h. Increasing the catalyst layer thickness leads to higher oxygen conversions in the reactor. This phenomenon can be observed especially in the ﬁrst part of the reactor. For both GHSV values and SS/TS = 9, the Da number, deﬁned as M V r Da = C2H4 cat 1 , is calculated and presented in Figure 4.39 as a function of M inlet dimensionless axial and radial coordinates. The coordinates are scaled by the reactor diameter. No internal and external transfer limitations are observed for both cases. The obtained tendencies can be explained by the insufﬁcient catalytic

129

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4 Transport Phenomena in Porous Membranes and Membrane Reactors

surface. By increasing the catalytic surface and the contact time in a thicker catalyst layer the conversion level in the reactor can rise signiﬁcantly. Residence time effects are observed in the simulations by varying the SS/TS ratio. The local residence time and the local and average oxygen concentration increase in the reactor tube at higher SS/TS ratios, followed by an increase in the ethane conversion. A longer residence time of the ethane molecules also promotes radial diffusion towards the catalyst layer. The obtained results show that the operating parameters like residence time, temperature and SS/TS ratio have a signiﬁcant inﬂuence on ethane conversion and ethylene yield. For effective operation of CMR, low total volume ﬂow rates and high SS/TS ratios are needed for higher conversions in the reactor. Increasing the inlet temperature leads to higher conversion and lower selectivity. Because the conversion is the limiting factor under the investigated conditions, its increase causes a rise in the ethylene yields. In the accomplished simulations, the concentration ratio was varied within a relatively small range. Nevertheless, a clear tendency of improving ethylene selectivity at lower oxygen concentration is observed. Based on this theoretical parameter study, a high potential for the CMR performance can be demonstrated. An application of this type of membrane reactor in mini- or micro-scale modules could be of great interest.

4.7 Conclusion

The presented results contribute to a better understanding of the coupled transport and reaction phenomena in membrane reactors. A signiﬁcant inﬂuence of the transport processes on the yield and the selectivity was observed, especially for the case of the catalytic membrane reactor (CMR). Optimal operation conditions for membrane reactors can only be achieved by selecting appropriate parameters. An analysis of the inﬂuence of operating parameters as well as that of the geometry and structural parameters of the membrane was made by numerical experiments, which led to important conclusions regarding this reactor type. More results regarding other membrane reactor conﬁgurations are presented in the following chapters.

References Alfonso, M.J., Julbe, A., Farrusseng, D., Menendez, M., and Santamaria, J. (1999) Oxidative dehydrogenation of propane on V/γ-Al2O3. Chem. Eng. Sci., 54, 1265–1272. Byrd, R.H., Lu, P., Nocedal, J., and Zhu, C. (1995) A limited memory algorithm for

bound constrained optimization. SIAM J. Sci. Comput., 16 (5), 1190– 1208. Cussler, L. (1997) Diffusion, Mass Transfer in Fluid Systems, Cambridge University Press.

References Edreva, V., Zhang, F., Mangold, M., and Tsotsas, E. (2009) Mass transport in multilayer, porous metallic membranes: diagnosis, identiﬁcation and validation. Chem. Eng. Technol., 32 (4), 632–640. Georgieva-Angelova, K. (2008) Modellbasierte Analyse der Transportprozesse und des Einﬂusses der Betriebs- und Geometrieparameter in einem katalytisch beschichteten Membranreaktor, PhD Thesis, University of Magdeburg. Girault, V., and Raviart, P.-A. (1986) Finite Element Methods for Navier-Stokes Equations, Springer, Berlin. Goering, H. (1977) Asymptotische Methoden zur Lösung von Differentialgleichun-gen, Akademie-Verlag, Berlin. Hamel, Ch. (2008) Experimentelle und modellbasierte Studien zur Herstellung kurzkettiger Alkene sowie von Synthesegas unter Verwendung poröser und dichter Membranen, Docupoint Verlag Magdeburg. Hein, S. (1999) Modellierung wandgekühlter katalytischer Festtbettreaktoren mit Ein- und Zweiphasenmodellen, VDI-Verlag, Düsseldorf. Hussain, A. (2006) Heat and mass transfer in tubular inorganic membranes, PhD Thesis, Otto-von-Guericke-University Magdeburg. Hussain, A., Seidel-Morgenstern, A., and Tsotsas, E. (2006) Heat and mass transfer in tubular ceramic membranes for membrane reactors, heat and mass transfer in tubular ceramic membranes for membrane reactors. Int. J. Heat Mass Transf., 49, 2239–2253. John, V., Knobloch, P., Matthies, G., and Tobiska, L. (2002) Non-nested multi-level solvers for ﬁnite element discretizations of mixed problems. Computing, 68, 313–341. Keil, R. (2007) Modeling of Process Intensiﬁcation, Chapter 5, Packed-bed Membrane Reactors, Wiley-VCH Verlag GmbH, Weinheim. Klose, F. (2008) Structure-Activity Relations of Supported Vanadia Catalysts and the Potential of Membrane Reactors for the Oxidative Dehydrogenation of Ethane, Docupoint Verlag Magdeburg. Knobloch, P., and Tobiska, L. (2008) On the Stability of the Finite Element Discretization

of Convection-Diffusion-Reaction Equations, Preprint 08–11, Otto-von-GuerickeUniversity Magdeburg. Kramers, H.A., and Kistemaker, J. (1943) On the slip of a diffusing gas mixture along the wall. Physica, 10, 699–713. Krasnyk, M., Bondareva, K., Mikholov, O., Teplinskiy, K., Ginkel, M., and Kienle, A. (2006) The ProMoT/Diana simulation environment, in Proc. of the 16th European Symposium on Computer Aided Process Engineering (ed. W. Marquardt and C. Pantelides), Elsevier, pp. 445– 450. Matthies, G., and Tobiska, L. (2007) Mass conservation of ﬁnite element methods for coupled ﬂow-transport problems. Int. J. Comput. Sci. Math., 1, 293–307. Matthies, G., Skrzypacz, P., and Tobiska, L. (2005) Superconvergence of a 3D ﬁnite element method for stationary Stokes and Navier-Stokes problems. Numer. Methods Part. Diff. Equat., 21, 701–725. Matthies, G., Skrzypacz, P., and Tobiska, L. (2007) A uniﬁed convergence analysis for local projection stabilization applied to the Oseen problem. ESAIM: M2AN, 41 (4), 713–742. Matthies, G., Skrzypacz, P., and Tobiska, L. (2008) Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions. ETNA, 32, 90–105. Rodriguez-Fernandez, M., Mendes, P., and Banga, J.R. (2006) A hybrid approach for efﬁcient and robust parameter estimation in biochemical pathways. BioSystems, 83 (2–3), 248–265. Roos, H.-G., Stynes, M., and Tobiska, L. (2008) Robust Numerical Methods for Singularly Perturbed Differential Equations. Convection-Diffusion-Reaction and Flow Problems, Springer Series in Computational Mathematics, vol. 24, Springer-Verlag, Berlin. Schlünder, E.U., and Tsotsas, E. (1988) Wärmeübertragung in Festbetten, durchmischten Schüttgütern und Wirbelschichten, Georg Thieme Verlag, Stuttgart. Skrzypacz, P., and Tobiska, L. (2005) Finite element and matched asymptotic expansion methods for chemical reactor

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4 Transport Phenomena in Porous Membranes and Membrane Reactors ﬂow problems. Proc. Appl. Math. Mech., 5, 843–844. Teplinskiy, K., Trubarov, V., and Svjatnyj, V. (2005) Optimization problems in the technological-oriented parallel simulation environment, in Proc. of the 18th ASIM-Symposium on Simulation Techniques (eds. F. Hülsemann et al.) SCS Publishing House, Erlangen, pp. 582–587. Thomas, S. (2003) Kontrollierte Eduktzufuhr in Membranreaktoren zur Optimierung der Ausbeute gewünschter Produkte in Parallel- und Folgereaktionen. Logos Verlag, Berlin. Turek, S. (1999) Efﬁcient Solvers for Incompressible Flow Problems, Lecture Notes in Computational Science and Engineering, vol. 6, Springer-Verlag, Berlin.

Uchytil, P., Schramm, O., and SeidelMorgenstern, A. (2000) Inﬂuence of the transport direction on gas permeation in two-layer ceramic membranes. J. Membr. Sci., 170 (2), 215–224. Ullmann (1977) Ullmann’s Encyclopädie Der Technischen Chemie, Verlag Chemie, Weinheim. Young, J.B., and Todd, B. (2005) Modelling of multi-component gas ﬂows in capillaries and porous solids. Int. J. Heat Mass Transf., 48, 5338–5353. Zanﬁr, M., and Gavriilidis, A. (2003) Catalytic combustionassisted methane steam reforming in a catalytic plate reactor. Chem. Eng. Sci., 58, 3947–3960. Zhang, F. (2008) Model identiﬁcation and model based analysis of membrane reactors, PhD thesis, Otto-von-GuerickeUniversität, Magdeburg.

133

5 Packed-Bed Membrane Reactors Christof Hamel, Ákos Tóta, Frank Klose, Evangelos Tsotsas, and Andreas Seidel-Morgenstern 5.1 Introduction

In the ﬁeld of chemical reaction engineering intensive research is devoted to developing new processes for many industrially relevant reactions in order to improve the selectivities and yields of intermediate products (e.g., partial oxidations; Hodnett, 2000; Sheldon and van Santen, 1995). Chapter 1 describes how in reaction networks optimal local reactant concentrations are essential for a high selectivity towards the target product (Levenspiel, 1999). If undesired series reactions can occur, it is usually advantageous to avoid backmixing. This is one of the main reasons why partial hydrogenations or oxidations are preferentially performed in tubular reactors (Westerterp, Swaaij, and Beenackers, 1984). Typically, all reactants enter such reactors together at the reactor inlet (co-feed mode). Thus, in order to inﬂuence the reaction rates along the reactor length, essentially temperature is the parameter that could be modulated. In classic papers, summarized by (Edgar and Himmelblau, 1988), the installation of adjusted temperature proﬁles has been suggested in order to maximize selectivities and yields at the reactor outlet. However, the practical realization of a deﬁned temperature modulation is not trivial. Alternative efforts have been devoted to study the application of distributed catalyst activities (Morbidelli, Gavriilidis, and Varma, 2001). This can be realized, for example, by mixing different catalysts or by local catalyst dilution. An attractive option, which is also capable to inﬂuence the course of complex reactions in tubular reactors and which is discussed in this chapter, is to abandon the conventional co-feed mode and to install more complex dosing regimes. The concept is based on the fact that there is a possibility to add one or several reactants to the reactor in a distributed manner. There is obviously a large variety of options differing mainly in the positions and amounts at which components are dosed. Deciding whether a certain concept is useful or not requires a detailed understanding of the dependence of the reaction rates on concentrations. As discussed in Chapter 1 in particular the reaction orders with respect to the dosed component are of essential importance (Lu et al., 1997a, 1997b, 1997c). Besides dosing one or several components at a discrete position into a ﬁxed-bed Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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reactor there also exists the possibility to realize a distributed reactant feeding over the reactor wall. This can be conveniently realized using tubular membranes. The concept of improving product selectivities in parallel-series reactions by feeding one reactant through a membrane tube into the reaction zone was studied, for example, by (Coronas, Menendez, and Santamaria, 1995; Diakov and Varma, 2004; Hamel et al., 2003; Kürten, Sint Annaland, and Kuipers, 2004; Lafarga, Santamaria, and Menéndez, 1994; Lu et al., 2000; Seidel-Morgenstern, 2005; Tota et al., 2004; Zeng, Lin, and Swartz, 1998). Theoretical and laboratory-scale studies focusing on the application of various conﬁgurations of membrane reactors described in Chapter 1 in order to improve selectivity–conversion relations in complex reaction systems are available. In particular, several industrially relevant partial oxidation reactions were investigated. Relevant studies were performed, for example, for the oxidative coupling of methane (Caro et al., 2006; Diakov, Lafarga, and Varma, 2001; Tonkovich et al., 1996a), for the partial oxidation of ethane (Al-Juaied, Lafarga, and Varma, 2001; Coronas, Menendez, and Santamaria, 1995; Klose et al., 2004a; Klose et al., 2003a; Wang et al., 2006) and propane (Caro, 2006; Grabowski, 2006; Liebner et al., 2003; Ramos, Menendez, and Santamaria, 2000; Schäfer et al., 2003; Ziaka, Minet, and Tsotsis, 1993) and for the oxidative dehydrogenation (ODH) of butane (Alonso et al., 2001; Mallada et al., 2000b; Tellez, Menendez, and Santamaria, 1997). In most of these works a single tubular membrane was used to distribute one reactant in the inner volume ﬁlled with catalyst particles. In this contribution the partial oxidations of ethane to ethylene and propane to propylene as model reactions performed in a pilot-scale membrane reactor were investigated in detail. For such reactions improved integral reactor performance can be achieved further by an optimized stage-wise dosing of one or several reactants (Hamel et al., 2003; Thomas, 2003). Adjusted dosing proﬁles can be realised, for example, by feeding reactants separately through permeable reactor walls (e.g., through tubular membranes discussed in Chapter 4).

5.2 Principles and Modeling 5.2.1 Reactant Dosing in a Packed-Bed Membrane Reactor Cascade

Figure 5.1 shows schematically the principle of the well established packed-bed reactor (PBR) in comparison to a three-stage membrane reactor cascade (PBMR-3) applied for controlled multi-stage dosing of reactants through the reactor wall, respectively. The three-stage membrane reactor cascade allows the realization of different dosing proﬁles, distributing the fed amount of reactants in the particular stages, inﬂuencing the local concentration and residence time of the reactants.

5.2 Principles and Modeling

Packed-bedreactor CnHm N2 O2

O2 N2 CnHm N2 O2 N2

CnHm-2 N2 O2 10% 33% 60% JO2

Membrane reactor cascade

for a multi stage reactantdosing 30% 33% 30% JO2

60% 33% 10% JO2

CnHm-2 N2 O2

Figure 5.1 Reactant feeding in a packed-bed reactor (PBR) and in a multi-stage membrane reactor (PBMR) cascade.

The reactants are fed separately in the packed-bed membrane reactor (PBMR) on the inner side (tube side, TS) and outer side (shell side, SS) of the membrane. The catalyst is placed in the tube side of the membrane as a packed bed. The applied dead-end reactor conﬁguration allows a feeding of reactants through the membrane in a controlled manner, with deﬁned ﬂuxes. All reactants dosed have to permeate through the membrane, which is considered to be catalytically inert. The membrane reactor illustrated in Figure 5.1 differs from the conventional PBR with respect to local residence time, local concentration and temperature proﬁles. Figure 5.2a depicts typical total ﬂow rates for PBR and PBMR for identical overall feed ﬂow and outlet ﬂow rates without chemical reaction, respectively. In this schematic representation the total ﬂow rate in the PBR remains constant along the reactor length. All reactants are fed in a co-feed mode at the reactor entrance and have, therefore, the same average residence time in the reactor. For comparison, PBMR proﬁles are shown for two different ratios of tube side to shell side ﬂow rate (FTS/FSS = 1 : 8 and/or 1 : 1). Assuming a uniformly distributed ﬂux through the membrane there is a linear increase in the total ﬂow rate along the reactor length. The slope decreases as the FTS/FSS ﬂow ratio increases. This causes a decreasing residence time of the reactants at the entrance of the reactor. Reactants fed via the shell side have a different residence time distribution. Due to the fact that reactants entering the reaction zone next to the inlet pass a longer reactor distance than molecules entering close to the outlet, the average residence time of the reactants dosed in a PBMR through the membrane is higher compared to a PBR (Tonkovich et al., 1996b). Thus, a higher conversion can be expected in a PBMR. Additionally to a one-stage membrane reactor a multi-stage cascade allows a feeding of different amounts as well as suitable dosing proﬁles in each stage. Just like the residence time behavior, the local concentrations of the reactants inﬂuences the reactor performance signiﬁcantly. The local concentration has an inﬂuence on local reaction rates as well as on conversion and selectivity. Demonstrating the differences between the reactor concepts, Figure 5.2b reveals the internal oxygen concentration proﬁles. Hereby the total amount of oxygen

135

(a)

TS/SS -1/8

TS/SS -1/1

PBR

6 5 4

TS/SS

3 2

t

1 0 0

0.2

0.4

0.6

0.8

1

(b)

0.06

Concentration O2

5 Packed-Bed Membrane Reactors

Totalflowrate

136

0.05

TS/SS -1/8

TS/SS -1/1

PBR

0.04

TS/SS

0.03 0.02

o2

0.01 0 0

0.2

z/L [-]

0.4

0.6

0.8

1

z/L [-]

Figure 5.2 Schematic illustration of: a) total ﬂow rates and b) molar fraction of oxygen in a ﬁxed-bed reactor (PBR) and in a membrane reactor (PBMR) for two different tube side/shell side feed ﬂow ratios (TS/SS).

dosed over the membrane in the PBMR is the same as for the PBR. Without the occurrence of chemical reactions in the PBR the molar fraction of oxygen is constant along the reactor length. Considering the ODH of short-chain alkanes, a high oxygen level is undesirable because it favours the consecutive reactions (Hamel et al., 2003; Klose et al., 2003b; Tota et al., 2004). Via distributed feeding the local oxygen concentration can be reduced in a membrane reactor, as shown in Figure 5.2b. Thus, the selectivity of desired intermediate products should be increased by avoiding series reactions. At low FTS/FSS ratios (i.e., for high trans-membrane ﬂuxes) the concentration of oxygen increases rapidly at the entrance. The local and hence also the averaged oxygen concentration is always lower than in the PBR. It is worthwhile to note that, under these ﬂow conditions, the local residence time of the hydrocarbons is relatively high near the PBMR inlet. This behavior will also, together with the rapidly increasing oxygen concentration, signiﬁcantly inﬂuence the temperature proﬁles in the reactor. 5.2.2 Modeling Single-Stage and Multi-Stage Membrane Reactors 5.2.2.1 Simpliﬁed 1-D Model The main advantage of reduced 1-D pseudo-homogeneous models is that they are computationally inexpensive (see Chapters 1 and 2, respectively). Comprehensive parametric studies can be carried out within a few minutes, which makes this model attractive for optimization calculations. A reduced reactor model was applied for an efﬁcient calculation and evaluation of PBR and PBMR in a broad range of operation conditions (Caro et al., 2006; Hamel et al., 2006; Hamel et al., 2003; Tota et al., 2004). The simpliﬁed “1-D model” allows analysis of a series connection of S equally sized stages of isothermal tubular reactors, as illustrated in Figure 5.1. All reactants can be dosed in a discrete manner in each stage s at the inlets (ρ gTSy iTS FTTS )s ,mix and/or

5.2 Principles and Modeling

over the walls (jiTS,s). Every reactor stage is modeled under the following conditions: negligible axial and radial dispersion, plug ﬂow, steady-state and isothermal operation. Based on these assumptions the mass balance for stage s can be written as: NR is d ( ρ gTSy iTSFTTS ) dm i ∑ ν ijr j + A TS jiTS,ss with j = 1, N R ; s = 1, S (5.1) = s = VR ρcatM s dξ dξ j =1 s

In Equation 5.1 ξ s = zs/Z is the dimensionless length coordinate and jiTS,s is, in contrast to the 1+1-D model presented below, the constant convective ﬂux of component i over the wall of stage s. The following boundary conditions were used together with Equation 5.1: i1 (ξ1 = 0 ) = m iin m

(5.2)

is (ξ s = 0 ) = m is −1 (ξ s −1 = 1) + m is ,mix m

(5.3)

The total amounts of component i introduced at all inlets (mix, S ≥ 2) and over all walls (diff ) are: S

imix is ,mix m ,tot = ∑ m

(5.4)

k =2 S

S

s =1

s =1

idiff is ,diff = A TS ∑ jiTS,s m ,tot = ∑ m

(5.5)

With the exception of a few cases (simple reaction orders, isothermal condition), the solution of the above system of ordinary differential equations can be performed only numerically. For this there are several numerical software tools available. In this contribution Matlab® was used to solve the initial value problem given in Equations 5.1–5.5. 5.2.2.2 More Detailed 1+1-D Model The assumption of a purely pressure-driven convective ﬂow through the membrane is usually an adequate approximation, even in laboratory-scale reactors. However, if the barrier effect exerted by the membrane is insufﬁcient, that is, diffusive transport in the pores (e.g., bulk, Knudsen, or surface diffusion) cannot be neglected, transport equations must be deﬁned for the membrane and solved simultaneously with the balance equations for both sides of the membrane. Such a scenario is analyzed in the following. In this study a simpliﬁed transport model, the so-called extended Fick model (EFM) was used to describe the mass transport of the species through the membrane. Compared to the more sophisticated dusty gas model (DGM; Chapters 2 and 4; Mason and Malinauskas, 1983) the interactions between the species are treated on a much simpler way in this modeling approach. The mass ﬂux of a component i is given by:

ji = −Di ,eff ρ g

∂y i B ∂p − yi ρg 0 . ∂r η ∂r

(5.6)

137

138

5 Packed-Bed Membrane Reactors Table 5.1 Simulation parameters for the 1+1-D reactor models (5.6–5.14).

Reactor length (length of the porous zone) –L Inner/outer diameter of the membrane –di/do Membrane permeability –B0 Knudsen coefﬁcient –K0 Membrane porosity to tortuosity ratio –ε/τ Membrane pore diameter –dpor W/F Oxygen concentration (overall) Ethane concentration (overall) Tube to shell side ﬂow ratio –FTS/FSS Reactor temperature

60 mm 7/10 mm 5.4e−14 m2 9.6e−08 m 0.096 3 μm 150–225–400 kg s/m3 2 vol% 2 vol% 2/1–1/1–1/4–1/9 600 °C

The effective diffusion coefﬁcient Di,eff is calculated by means of Equation 2.57 discussed in Chapter 2. The second term on the right hand side of Equation 5.6 is the convective ﬂux, where according to Darcy’s law the superﬁcial velocity is expressed by the pressure gradient. The membrane is characterized by three structure parameters (B0, εp/τ, K0) which have to be obtained experimentally (Table 5.1 and Chapter 4). The 1+1-D reactor model has been derived based on the following assumptions:

• • • •

Isothermal, steady-state conditions, ideal gas behavior, Constant total pressure and plug-ﬂow on TS and SS, Absence of mass transport limitations, reactions only occur on the TS, Molecular and Knudsen diffusion with superimposed convective ﬂux through the membrane.

The mass balances as well as the corresponding boundary conditions are given below:

•

Component mass balance on the “tube side” (TS): NR ∂ TS TS TS ( ρ g yi FT ) = VR ρcat ⋅ M i ∑ νijr j + A TS jiTS (z ) for i = 1, … , NC ∂z j =1

•

Overall mass balance: NC ∂ TS TS ( ρ g FT ) = ∑ A TS jiTS (z ) ∂z i =1

•

(5.8)

Boundary conditions on TS: TS TS TS TS y iTS z = 0 = y iTS ,0 ; ρ g FT z = 0 = ρ g ,0FT ,0

•

(5.7)

(5.9)

Component mass balance on the “shell side” (SS): ∂ SS SS SS ( ρ g yi FT ) = ASS jiSS (z ) for i = 1, … , N C ∂z

(5.10)

5.2 Principles and Modeling

•

Overall mass balance: NC ∂ SS SS ( ρ g FT ) = ∑ ASS jiSS (z ) ∂z i =1

•

Boundary conditions on SS: SS SS SS y iSS z = 0 = y iSS,0 ; ρSS g FT z = 0 = ρ g ,0FT ,0

•

(5.12)

Mass balance for the membrane: 1 ∂ (r ⋅ ji ) = 0 for i = 1, … , N C r ∂r

•

(5.11)

(5.13)

Boundary conditions for the membrane: yi

r = ri

= y iTS and y i

r = ro

= y iSS , p r = ro = pSS and p r = ri = pTS

(5.14)

These algebraic equations are coupled by the boundary conditions to the system of ordinary differential equations for TS and SS, respectively. The resulting nonlinear differential algebraic equation system was solved using Newton iterations and the direct linear solver UMFPACK in Comsol Multiphysics 3.2 (COMSOL, 2006). For the applied dead-end membrane reactor conﬁguration the SS pressure was found by an iterative procedure. 5.2.2.3 Detailed 2-D Modeling of a Single-Stage PBMR For a theoretical analysis a detailed 2-D reactor model assuming steady-state, ideal gas behavior, no heat and mass transfer limitations between bulk phase and catalyst particle as well as inside the catalyst pellets was developed and implemented in the simulation tool Comsol. This model is based on the Equations 2.7–2.11 presented in Chapter 2 and by (Tota et al., 2007), respectively. Important parameters for packed-bed membrane reactors are the effective radial and axial heat dispersion coefﬁcients, which were calculated according to two different approaches described by (Tsotsas, 2002). The ﬁrst approach called “αw model” presumes heat dispersion with different but radially constant coefﬁcients in both directions. The second one, called “λ(r) model”, was developed by (Cheng and Vortmeyer, 1988) and reﬁned in an extensive comparison with experimental data by (Winterberg and Tsotsas, 2000b; Winterberg et al., 2000). The authors argued that especially in reactive ﬂow problems at low Reynolds numbers the assumption of an inhibiting laminar sublayer at the wall is not appropriate. Therefore, the use of a wall heat transfer coefﬁcient, αw, can only be artiﬁcial. The correlations applied for the calculation of the radial/axial heat dispersion coefﬁcient are given by (Tota et al., 2007; Winterberg and Tsotsas, 2000a). To calculate the ﬂow ﬁeld under reactive conditions the extended Navier–Stokes equation and the mass continuity equation deﬁned in Chapter 2 (2.7–2.8) were solved. Regarding the boundary conditions for the membrane reactor, there is one considerable difference compared to the PBR: the radial component of the velocity at the membrane wall is not zero. The latter is proportional to the trans-membrane ﬂux. The friction force arising due to the ﬂow through the packed bed can be

139

140

5 Packed-Bed Membrane Reactors

calculated according to (Ergun, 1952) by deﬁning the friction coefﬁcient. For low tube-to-particle diameter ratios a signiﬁcant part of the ﬂow shifts from the core of the bed towards the reactor wall. This so-called ﬂow maldistribution is caused by the non-uniform porosity proﬁle of the packed bed. The effect on the local velocity is pronounced especially at low-particle Reynolds numbers (Winterberg and Tsotsas, 2000b). To describe the experimentally found damped oscillation of the radial porosity proﬁles, the correlation given by (Hunt and Tien, 1990) was applied.

5.3 Model-Based Analysis of a Distributed Dosing via Membranes 5.3.1 Model Reactions

As model reactions the oxidative dehydrogenation (ODH) of ethane to ethylene and the ODH of propane to propylene on a VOx/γ-Al2O3 catalyst were chosen. A detailed analysis of the networks and the ﬁve main reactions taking place is given by (Klose et al., 2004b), (Liebner, 2003), and in Chapter 3 of this book respectively. According to the scheme given in Figure 5.3a, ethane is converted in a parallel reaction to CO2 and the desired product ethylene. This parallel reaction limits the maximal achievable ethylene selectivity in the reaction (Klose et al., 2004a). Additionally, the consecutive reaction to CO and the total oxidation can further decrease the oleﬁn selectivity. The authors suggested a kinetic model based on a Mars–van Krevelen type redox mechanism for the ethylene production and Langmuir–Hinshelwood–Hougen–Watson kinetics for the deep oxidation reactions (Joshi, 2007; Klose et al., 2004a). The derived kinetic model for the ODH of ethane was found to describe a large set of experimental laboratory-scale data with good accuracy (see Chapter 3). In principle the reaction network of propane, given in Figure 5.3b, is similar. Also propane is converted in a parallel reaction to CO2 and the desired product propylene. According to the studies of (Liebner, 2003), propylene can be formed,

(a) +0.5 O2 r1

C2H4 desired

+3.5 O2 r2

+3 O2

CO2

r4 r5

r3

+2 O2

+0.5 O2

CO Figure 5.3

(b)

C2H6

-H2 r5

C3H6 desired +3 O2

C2H8 r1 +0.5 O2

r2

+5 O2

CO2 r3

CO

+H2O r4 +H2

Reaction network of the oxidative dehydrogenations of ethane and propane.

5.3 Model-Based Analysis of a Distributed Dosing via Membranes

141

respectively, by ODH (r1) and by the thermal dehydrogenation of propane (r5) in the absence of oxygen. In contrast to the ethane network and considering the lower temperature range the ratio of CO and CO2 is determined by the water gas shift reaction. 5.3.2 Simulation Study for ODH of Ethane Using the 1-D Model

(a)

Selectivity C2H4 [%]

C

A

B

D

Conversion C2H6 [%]

This section investigates the performance of a conventional PBR and a single-stage membrane reactor in a simulation study and compares the results for the ODH of ethane to illustrate the reactor behavior in a broad range of operating conditions. Therefore the reduced membrane reactor model given by Equations 5.1–5.3 for one-stage, as well as the reaction rates given by (Klose et al., 2004b) were applied. As shown in Figure 5.4a, the single-stage PBMR shows a higher ethylene selectivity than the PBR in the oxygen-controlled region for a high mass of catalyst/ total ﬂow rate (W/F) corresponding to a high conversion. Increasing the oxygen level decreases the ethylene selectivity. Because of unavoidable uncertainties of the

(b)

PBR PBMR

xO2 [-] W/F [kgs/m³]

xO2 [-]

W/F [kgs/m³] (c)

Yield C2H4 [%]

PBR C2H6 N2 O2

O 2,N 2 C2H6,N 2

xO2 [-]

³] gs/m k [ F

C2H4 N2 O2

PBMR JO2

O 2,N 2

W/

Figure 5.4 Comparison between PBR and PBMR: a) selectivity of ethylene, b) conversion of ethane, c) yield of ethylene. xC2H6in = 1.5%, xO2in = 0.5–21.0%, W/F = 50–550 kg s/m3, T = 600 °C, FTS/FSS = 1/8.

C2H4 N2 O2

5 Packed-Bed Membrane Reactors

kinetic model the simulation results below an oxygen level of 1 vol% should be evaluated with care. In the conversion plot given in Figure 5.4b the beneﬁts of the PBMR can be recognized. Conversion differences of up to 15% can be obtained for a broad range of oxygen concentration and residence time. Below an oxygen concentration of 1.5 vol% the PBR shows slightly higher conversions, which can be explained by the higher local oxygen concentration in the PBR. This region is extended towards higher oxygen concentrations with increasing residence time. Differences in the mean residence time of the reactants between PBR and PBMR are still present, but not so signiﬁcant as below W/F = 250 kg s/m3. With increasing contact time the oxygen level is the only conversion-determining factor. The resulting ethylene yields (Figure 5.4c) reveal that there are two preferable regions for the application of a PBMR. The ﬁrst one is in the residence time-controlled region (in this case below approximately 250 kg s/m3). In this region the oxygen concentration can be relatively high. The higher ethylene yields achievable here result from the high reactant conversion. The second region, where simulation postulates the highest PBMR yields, is at longer contact times for oxygen concentrations below 1.5 vol%. Finally, a comparison between the dosing concepts will be given by means of a selectivity–conversion plot. To get an insight into the selectivity behavior of the PBMR for the whole parameter range studied, one can extract all the simulation results for ethylene selectivity and ethane conversion and plot the corresponding values together in one diagram (Figure 5.5). The resulting envelope describes the attainable region for the reactor at 600 °C, for the ﬂow rates and reactant concentrations considered. In this special case the borders of the envelope are the edges indicated in Figure 5.4a as lines A, B, C and D. The results given in Figure 5.5 show that for low residence times (line C) and at high oxygen concentration (line D) the PBMR outperforms the PBR. However, in this region the yields are

70

Selectivity C2H4 [%]

142

A

60 50

D C

40

B

30 20 10

20

30

40

50

60

70

80

90

Conversion C2H6 [%] Figure 5.5 Ethylene selectivity versus ethane conversion in a ﬁxed-bed und one-stage membrane reactor; xC2H6in = 1.5%, xO2in = 0.5– 21.0%, W/F = 50–550 kg s/m3, T = 600 °C,

FTS/FSS = 1/8. A, B, C, and D are related to lower and upper limits of parameter ranges with respect to oxygen concentration and residence time.

5.3 Model-Based Analysis of a Distributed Dosing via Membranes

quite low in both reactors. Further, the curves of the PBMR are located within the operating window of the PBR; thus, one can easily ﬁnd operating parameters where the PBR is superior to the PBMR. For ethane per pass conversion below approximately 65% the PBR allows higher ethylene selectivity and therefore higher yields. If higher per pass conversions are needed, the reaction should be carried out in a PBMR, because the ethylene selectivity does not decrease as rapidly as in the reference concept (PBR). The maximal ethylene yields, marked by dots, are hardly different in the two reactors. According to the simulation result, 25.2% of the fed ethane is converted to ethylene for the chosen simulation conditions. This is achieved in the membrane reactor for around 10% higher conversion, while the ethylene selectivity is approximately 7% below that of the PBR. The following section presents simulation results of the 1+1-D reactor model, describing the laboratory-scale membrane reactor used (see chapter 5.4.2). For the sake of simplicity, the calculations are carried out for a homogeneous membrane with a pore diameter of 3 μm, and a typical membrane support with structure parameters is summarized in Table 5.1 (Hussain, 2006; Thomas, 2003). Figure 5.6a,b

3

3

xiSS [%]

(b) 4

xiTS [%]

(a) 4

2

1

1

0 0

2

0.25

0.5

0.75

1

0 0

0.25

0.5

0.75

1

z/L

z/L (b) 0.7

O2/C2H6 [-]

0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.25

0.5

0.75

1

z/L Figure 5.6 Comparison of simulation results for the 1-D (dashed) and the 1+1-D (solid) reactor model. Axial ethane (black), O2 (dark gray), ethylene (light gray).

Concentration proﬁles on: a) TS and b) SS. c) Oxygen to ethane concentration ratio on: W/F = 400 kg s/m3, T = 600 °C, xC2H6in = 2%, xO2in = 2%, FTS/FSS = 1/1.

143

5 Packed-Bed Membrane Reactors 70

Selectivity C2H4 [%]

144

150 65

225 60

55 400

50 20

30

40

50

60

Conversion C2H6 [%] Figure 5.7 Comparison of simulation results for the 1-D (dashed) and the 1+1-D (solid) reactor model. Conditions: W/F = 150/225/400 kg s/m3, T = 600 °C, xC2H6in = 2%, xO2in = 2%, FTS/FSS = 2/1–1/9.

illustrates axial concentration proﬁles of the reactants and ethylene on both membrane sides. These results correspond to extremely low trans-membrane pressure differences of approximately 50 mbar. It can be seen that the simple model given by Equations 5.7–5.14 (dashed line) gives higher local ethane concentrations than the more realistic 1+1-D reactor model (solid line). According to this model relatively high ethane and even ethylene concentration can be expected on the SS. At the same time the diffusive ﬂux considerably enhances the transport of oxygen through the membrane. This results in a high local oxygen to ethane concentration ratio (Figure 5.6c) and is responsible for the higher ethane conversions. The results suggest that the simpler model (5.1–5.3) underestimates the achievable ethylene yields in the membrane reactor. As a check simulations were carried out for higher trans-membrane pressure differences by changing the total ﬂow rate and FTS/FSS ﬂow ratio. As expected, the results show (Figure 5.7) that, at short contact times (W/F = 150 kg s/m3), both models give an almost identical reactor performance. Small discrepancies can be seen only by dominating tube side ﬂow conditions (FTS/FSS > 0.5). In these cases a slightly higher ethylene selectivity is to be expected. With increased contact time (W/F = 225 and 400 kg s/m3) the difference between the models increases. Ethane conversion increases, while a slight increase of the calculated ethylene selectivity is obtained. These results reveal that for the calculated laboratory-scale PBMR using a thin membrane thickness of 1.5 mm above approx. 200 kg s/m3 space time the more complex model should be used to compare reactor concepts. In cases where the membrane transport is dominated by the viscous ﬂow, the simple 1-D model can give sufﬁciently accurate results for a ﬁrst comparison.

5.4 Experimental

5.4 Experimental 5.4.1 Catalyst and Used Membrane Materials

As described in Chapter 3 the VOx/γ-Al2O3 catalyst used in this study for the ODH of ethane and propane in all reactors was prepared by soaking and impregnation of γ-Al2O3 with a solution of vanadyl acetylcetonate in acetone followed by a calcination step at 700 °C. The vanadium content of the catalyst was 1.4% V. The surface of the calcinated catalyst was 158 m2/g, measured by the single-point BET method. The color of the fresh catalyst is yellow, indicating that vanadium was mainly in the +5 oxidation state (Oppermann and Brückner, 1983). After the measurements, the catalyst color had changed to a light blue-green. This can be attributed to a signiﬁcant reduction of V(V) to V(IV). Ceramic (HITK e.v.) and sintered metal (GKN) membranes for oxygen dosing were investigated experimentally. The tubular ceramic composite membranes in a pilot-scale used for feeding air as the oxidant were provided by the Hermsdorfer Institut für Technische Keramik. They were already characterized in Chapter 4. They consisted of a mechanically stable α-Al2O3 support (average pore diameter: 3 μm; thickness: 5.5 mm) on which two more α-Al2O3 layers (pore diameters: 1 μm and 60 nm; thickness 25 μm) and ﬁnally one γ-Al2O3 layer were deposited (pore diameter: 10 nm; thickness: 2 μm). The whole membrane tube had a length of 350 mm and an inner/outer diameter of 21/32 mm. Both ends of the membrane were vitriﬁed, leaving in the center of the membrane a permeable zone of 104 mm (see Figure 5.8a). The mass transport properties of this membrane type were characterized by the authors in a previous study (Hussain, Seidel-Morgenstern, and Tsotsas, 2006). The sintered metal membranes were provided by GKN Sintered Metals Filters GmbH. These mechanically stable membranes are made of Inconel 600, and had a geometry similar to ceramic membranes (average pore diameter: 0.3 μm; thickness: 3 mm). During assembly of the membrane reactor, the membrane tubes were ﬁlled with inert material in the non-permeable zones and with the above-described VOx/γ-Al2O3 catalyst in the porous reaction zone. 5.4.2 Single-Stage Packed-Bed Membrane Reactor in a Pilot-Scale

In order to study a PBMR with radial dimensions close to an industrial scale, a pilot-plant was realized allowing total feed ﬂow rates up to 4500 L/h. Beside the possibility to evaluate the development of radial and axial gradients the large scale had the advantage that the impact of measuring installations, especially thermocouples within the catalyst bed, which disturb ﬂuid dynamics, was signiﬁcantly reduced. The single-stage PBMR consisted of a stainless steel tube (inner

145

146

5 Packed-Bed Membrane Reactors (a)

(b)

Figure 5.8 a) Porous asymmetric Al2O3 membrane (left) and sintered metal membrane (right). b) Multi-stage membrane reactor cascade for the oxidation of short-chain hydrocarbons on a pilot scale.

diameter: 38.4 mm) into which the membrane tube ﬁlled with catalyst was inserted. The reactor was heated by an electric heating sleeve outside the steel tube. The hydrocarbons, for safety reasons diluted 1 : 10 in nitrogen, were fed on the tube side of the membrane. Air was dosed from the shell side over the membrane into the reactor. The shell side outlet was closed so that all dosed air was pressed through the membrane into the catalyst bed (see Figure 5.1). This conﬁguration is similar to that reported most often in the recent literature, for example, by (Mallada, Menéndez, and Santamaría, 2000a; Ramos, Menendez, and Santamaria, 2000; Tonkovich et al., 1996b). However, it differs from those studies, where the shell side outlet was open, in that oxidant transfer over the membrane is inﬂuenced by diffusion (Farrusseng, Julbe, and Guizard, 2001; Kölsch et al., 2002). Pressing all air over the membrane has the advantage of an easy control of the amount of air inserted. In this way the membrane was used as a non-perm selective oxidant distributor in a “dead-end” conﬁguration. During assembly of the reactor the membrane tube was ﬁlled with inert material in the vitriﬁed zones and with VOx/γ-Al2O3 catalyst (17 g) in the permeable section. Five thermocouples were placed in the center of the tube: at the reactor inlet/outlet, at inlet/outlet of the porous zone and in the middle of the catalyst bed (see Figure 5.10a). Additionally, thermocouples were installed on the surface of the membrane on shell and tube side. Gas samples were taken at the tube side inlet and directly after the reactor outlet. The membrane tube was ﬁxed in housing with ﬁxed ﬂanges. Both mem-

5.4 Experimental

brane sides were sealed gas-proof by pressing the applied graphite seals (Novaﬁt) during the assembling of the slip-on ﬂanges at the ends. These ﬂanges had a distance of 125 mm from the hot reaction zone. Because of the material of the seals the upper head segment temperature was limited to 550 °C. It was possible to operate the reactor at catalyst temperatures up to 650 °C without any damage to the seals or the membrane itself. 5.4.3 Reference Concept – Conventional Fixed-Bed Reactor

For the ﬁxed-bed experiments the same reactor equipment was used as for the PBMR. A completely vitriﬁed alumina membrane with the same geometry was installed in the membrane reactor housing. All reactants were fed in a co-feed mode (Figure 5.1). The application of a vitriﬁed membrane avoids wall reactions compared to a simple ﬁxed-bed reactor made from stainless steel. Further it allows experiments to be performed under similar heat transfer conditions. 5.4.4 Multi-Stage Membrane Reactor Cascade

The membrane reactor cascade (PBMR-3) applied for studying the local concentration distribution of oxygen and the residence time behavior consists of a series connection of three identical membrane reactors, as described in the previous section and illustrated in Figure 5.1. The catalyst masses placed in every stage of the PBMR-3 were 17 g. The tube side outlet of each reactor was connected with the tube side inlet of the following reactor using a heated transfer line. The hydrocarbons were inserted in the tube side inlet of the ﬁrst reactor. Air was fed via a membrane from the shell sides of all reactors. To realise as different dosing proﬁles of air, for example, increasing (10/30/60%), uniform (33/33/33%) and decreasing (60/30/10%), the distribution of the overall air amount between the reactors was modiﬁed systematically. Further, each reactor could be heated separately by an electrical heating sleeve. However, for the experiments the temperature was kept equal in all the reactors. Gas sampling was possible at the tube side inlet of the ﬁrst reactor and at each tube side outlet of the three reactor stages. 5.4.5 Analytics

The set-up used consists of several units: reactor modules, catalytic afterburner and a gas chromatograph (Agilent 6890 GC/TCD with 5973 MSD) with a 12-port multiposition valve for reactant and product stream analysis. The catalytic afterburner had to prevent hazardous emissions to the environment. A SIMATIC S7based process control system was implemented to run the unit automatically and recover all process data. Feed mixtures and ﬂow conﬁgurations were realized by

147

148

5 Packed-Bed Membrane Reactors

using electronic mass ﬂow controllers (Bürkert, type 8712). Gas samples were taken from different positions of the reactors as described below by switching the multiposition valve. They were transferred via a heated line to the sample valve of the GC-MSD to prevent condensation. All gas samples were analyzed with a GC-TCD/MSD system equipped with a four-column conﬁguration. This conﬁguration included a HP Plot Q column for the quantiﬁcation of CO2, ethane/propane and ethylene/propylene, a HP Molsieve 5A column for the separation of permanent gases and CO and a FFAP column to analyze oxygenates. 5.4.6 Experimental Conditions

Based on the preliminary theoretical analysis shown above, a large set of experimental studies was carried out in a temperature range between 520–650 °C (ethane) and 350–500 °C (propane). The molar O2/CnH2n+2 ratio was varied between 0.5–5.0 and especially near the stoichiometric ratio (hydrocarbon/oxygen = 2 : 1) of the ODH of ethane. In the investigations, high space velocities were applied, closer to the requirements set by industry. The inverse weight hourly space velocity was varied between W/F = 100–400 kg s/m3 (catalyst mass/total volumetric ﬂow rate). Additionally, overall oxygen hydrocarbon ratios were kept below the lower explosion limit, which favored safety of operation. In all PBMR measurements the shell side/tube side feed ratio was adjusted at 8, meaning 88% of total feed ﬂow was permeated over the membrane. Hereby this ratio was kept constant independently on the dosed oxygen amount by mixing air with nitrogen for the permeating feed. The reproducibility was checked by conducting product stream analysis more than three times on every set of experimental parameters and additionally by twice repeating every complete run to examine additionally changes of the catalyst itself. The basic reference used to compare the performance of the reactors was the weight hourly space velocity, which was the same for all considered dosing strategies. Thus, the overall feed ﬂow rates of the PBMR-3 were related to the feed ﬂow rates of the PBR and PBMR, by applying a corresponding mass of catalyst.

5.5 Results for the Oxidative Dehydrogenation of Ethane to Ethylene 5.5.1 Comparison Between PBR and PBMR Using Ceramic Membranes in a Single-Stage Operation Mode

Figure 5.9a,c,e compares the performance of a single-stage PBMR using a ceramic membrane and a conventional PBR on a pilot scale for lean oxygen conditions (O2/C2H6 = 1), and Figure 5.9b,d,f does the same for excess oxygen conditions (O2/C2H6 = 5).

5.5 Results for the Oxidative Dehydrogenation of Ethane to Ethylene (a) 80 PBMR: 100

FBR: 100

PBMR: 400

FBR: 400

(b) 100 90

Conversion C2H6 [%]

Conversion C2H6 [%]

70 60 50

W/F

40 30 20 10

W/F

0 480

530

580

O22

630

80

PBMR: 100

FBR: 100

PBMR: 400

FBR: 400

70 60

W/F

50 40 30 20

W/F

10 0 480

680

530

Temperature [°C]

630

680

Temperature [°C]

(c) 80

(d) 80

Selectivity C2H4 [%]

Selectivity C2H4 [%]

580

O22

70

60

50

O22 40 480

530

580

630

70 60 50 40 30

O22

20 480

680

530

Temperature [°C] (f)

Selectivity C2H4 [%]

Selectivity C2H4 [%]

W/F

60

50

W/F

O22

630

680

Temperature [°C]

(e) 80 70

580

40

80 70

W/F

60 50 40 30

O22

W/F

20 0

10

20

30

40

50

60

70

Conversion C2H6 [%] Figure 5.9 a), b) Conversion of ethane versus temperature. c), d) selectivity of ethylene versus temperature. e), f ) Selectivity of ethylene versus conversion, ethane molar

0

20

40

60

80

100

Conversion C2H6 [%] fraction xC2H6in = 1.5%, O2/C2H6 = 1O2↓a.5O2↑, W/F = 100/400 kg s/m3, catalyst: VOX/γ-Al2O3, (1.4%), BET: 157 m2/g.

149

150

5 Packed-Bed Membrane Reactors

According to the simulations presented in the theoretical analysis above, a higher ethane conversion can be expected in the PBMR as long as the oxygen availability does not become rate-determining. This is due to the prolonged contact time of ethane over the catalyst bed compared to the PBR. Further, the parameter study revealed that, under oxygen excess conditions, the sensitivity of ethylene selectivity to oxygen partial pressure is low and for this reason, at moderate excess of oxygen, the PBMR should provide higher ethane conversion as well as higher ethylene yields. Figure 5.9a,b gives the impact of membrane-assisted oxidant dosing on ethane conversion under lean oxygen and excess oxygen conditions, respectively. For an excess of oxygen (Figure 5.9b) and high contact times (W/F > 100 kg s/m3) the PBMR outperforms the PBR signiﬁcantly. At short contact times (W/F = 100 kg s/m3) and low temperatures (below 600 °C) the conversions obtained in the PBMR and PBR are hardly different, as predicted by simulations. The enhanced conversion in the PBMR can be explained by the higher residence time induced by the distributed feeding of O2 and N2 over the membrane (see Section 5.2.1). In contrast, under lean oxygen conditions and for temperatures over 600 °C the PBR shows a better performance concerning conversion. For these operation parameters the PBMR seems to be limited with respect to oxygen. Thus, the dosed amount of O2 cannot be distributed radially over the catalyst bed. Latter aspect will be investigated in detail using 2-D reactor models. Higher conversions of ethane in the PBR can be obtained also at short contact times and at high temperatures. The selectivity of the desired intermediate product ethylene could be signiﬁcantly increased in the PBMR, especially for lean oxygen conditions, but also for conditions of oxygen excess and short residence times. Thus, the concept of decreasing the local oxygen concentration by distributed dosing to avoid series reactions forming CO and CO2 has proven to be successful applying ceramic membranes. For further information see Hamel et al., 2003; Thomas, Klose, and Seidel-Morgenstern, 2001. Under lean oxygen conditions ethylene selectivity can be signiﬁcantly enhanced using the PBMR at similar levels of ethane conversion (Figure 5.9e); in contrast under conditions of oxygen excess the selectivity–conversion plots fall together (Figure 5.9f ) with those of the corresponding PBR reference experiments. Thus, a beneﬁt regarding ethylene selectivity is given especially at low oxygen-tohydrocarbon ratios. A further intention of investigating membranes on a pilot scale was to study the developing radial temperature proﬁles. Thus, seven thermocouples were placed in the PBMR to measure the temperature at different positions of the catalyst bed and the membrane surface, respectively. The position of the thermocouples illustrated in Figure 5.10a was already described in Section 5.4. A more detailed analysis of the distributed dosing of reactants on the axial temperature proﬁles was alreadly given by (Tota et al., 2007). The study revealed that, for the PBMR, the heat transfer is characterized by heat conduction and additionally a high convective

Tcat out

Tout

21

Tcat in

32

Tin

(a)

Twall SS Twall TS Tcat

5,5

5.5 Results for the Oxidative Dehydrogenation of Ethane to Ethylene

123 175 227 350

(c) 625

(b) 625 Twallts

600

Temperature [°C]

Temperature [°C]

Tcat

575

Twallss 550

FBR: 1.5%O2 PBMR: 1.5%O2 FBR: 8%O2 PBMR: 8%O2

525

W/F W/F

500 0

5

10

15

Tcat

Twallts

600

Twallss

575 550

FBR: 1.5%O2 PBMR: 1.5%O2 FBR: 8%O2 PBMR: 8%O2

525 500

20

Radial reactor coordinate [mm]

0

5

10

W/F W/F 15

20

Radial reactor coordinate [mm]

Figure 5.10 a) Placement of thermocouples, b) temperature versus radial reactor coordinate (W/F = 400 kg s/m3), c) temperature versus radial reactor coordinate (W/F = 200 kg s/m3), xC2H6in = 1.5%.

radial ﬂow due to the distributed feeding of O2 and N2. Thus, the feed of the PBMR can be heated up more rapidly and/or the temperature can be controlled signiﬁcantly better than in co-feed mode in the PBR, where heat transfer takes place only by heat conduction over the reactor walls. The temperature regime with respect to the radial distribution is given in Figure 5.10b,c. As can be seen in Figure 5.10b at high contact times (W/F = 400 kg s/m3, low feed rates) the differences between PBMR and PBR are small, approximately 5 K. For a higher concentration of oxygen (8%) the temperatures at the shell side of the membrane wall (Twallss) are lower than in lean oxygen conditions in both reactor concepts. This is because the catalyst bed temperature Tcat is used as the control variable for the heating sleeves. A higher feed concentration of oxygen leads to an increase of the reaction rate, hence to enhanced heat generation. The latter is compensated by the controller, which is reducing the heating power of the heating jacket over the reactor length. In the case of higher feed ﬂow rates (W/F = 200 kg s/m3) the radial temperature gradients are small and can be neglected for the investigated membrane diameter (Figure 5.10c).

151

152

5 Packed-Bed Membrane Reactors

(a)

O2

x10-3

Length [m]

O2

Radius [m]

Radius [m]

(d)

(c)

(b) x10-3

Le ng th [m ]

O2

x10-3

Le ng th [m Radius [m] ]

O2

x10-3

Radius [m]

Figure 5.11 a), b) Simulated oxygen concentration ﬁelds in the PBMR, c), d) ethylene concentration using the λ(r) model. W/F = 400 kg s/m3, ethane molar fraction xC2H6in = 1.5%, O2/C2H6 = 1O2↓ and 5O2↑, T = 610 °C.

5.5.2 2-D Simulation Results – Comparison Between PBR and PBMR

Based on the detailed model presented in Chapter 2 the concentration, temperature and velocity ﬁelds in the PBMR were calculated. As selected results the calculated concentration ﬁelds of oxygen and the desired intermediate product ethylene using the “λ(r) model” are illustrated in Figure 5.11. The simulated concentration ﬁelds of oxygen (Figure 5.11a,b) illustrate clearly the PBMR principle: lowering the local oxygen concentration to avoid series reactions by membraneassisted distributed dosing. As shown in Figure 5.11a, under lean oxygen conditions and for temperatures over 600 °C the PBMR is limited with respect to oxygen. Thus, the dosed amount of O2 cannot be distributed radially in the whole catalyst provided. Consequently, the PBMR reveals under this condition a better performance concerning conversion. In contrast, for higher concentrations of oxygen (Figure 5.11b) the catalyst bed is used more efﬁciently, but the impact of series reactions increases, indicated by decreasing ethylene concentration (Figure 5.11c). Table 5.2 gives an overview with respect to the results of the reduced 1-D model (5.1–5.3) and the more detailed “αw model” and “λ(r)-model”, respectively, in comparison to the experimental data. The oxygen concentrations calculated with the 1-D model are considerably lower than those of the 2-D model. The predicted ethane conversion values (Table 5.2) are 3–7% higher. Thus, the lower oxygen concentration of the 1-D model results from higher oxygen consumption. Especially for high contact times (W/F = 400 kg s/m3), that is, low volumetric ﬂow rates as well as low Reynolds numbers, ethane conversion as well as ethylene selectivity could be described in a relatively good agreement with the detailed “λ(r) model”, taking into account the radial oxygen proﬁle and porosity distribution. This conclusion was also published by (Hein, 1999; Winterberg et al., 2000) especially for reactive conditions. For short contact times (W/F = 100 kg s/m3), that is, high

5.5 Results for the Oxidative Dehydrogenation of Ethane to Ethylene Evaluation of the detailed 2-D αw/λ(r) models and the reduced 1-D reactor model by means of experimental data: xC2H6in = 1.5%, xO2in = 8%, T = 610 °C.

Table 5.2

W/F [kg s/m3] Conversion C2H6 Selectivity C2H4 Yield C2H4

Experiment

1-D model

αw model

λ(r) model

[%]

[%]

[%]

[%]

100 33 60 20

400 72 34 25

100 36 49 18

400 79 30 24

100 32 50 16

400 66 32 21

100 32 51 16

400 72 33 24

Reynolds numbers, the applied “αw model” and “λ(r) model” are close together, as conﬁrmed by (Bey, 1998; Tsotsas and Schlünder, 1990) 5.5.3 Application of Sintered Metal Membranes for the ODH of Ethane

In spite of the performance improvement by membrane-assisted oxidant dosing, the drawback of a higher construction effort has to be addressed, too, and temperature resistant sealings of the membranes have to be found which should be safe and cost-effective. In this study graphite was used for sealing the ceramic membrane. One alternative can be the use of sintered metal membranes characterized in Chapter 4. Unfortunately, sintered metal membranes have much larger pores than ceramic ones. Thus, the trans-membrane pressure drop can be expected to be much lower than for mesoporous ceramic membranes. This is problematic on two counts. First, when the trans-membrane pressure drop is of the same order of magnitude as the pressure drop over the catalyst bed, the distribution of the reactants along the length is no longer uniform, which can signiﬁcantly affect the reactor performance (see also Section 5.5.4). Second, under the conditions of laboratory experiments, according to the theoretical analysis shown above, it seems impossible to compensate uncontrolled diffusive transport for the sintered metal membranes. Only at higher feed rates, when the dominating convective transport can be anticipated, does the application of sintered metal membranes seem to be attractive in the pilot plant. The sintered metal membrane (PBMR-SM) described in Section 5.4.1 was investigated under the same condition as the PBR and the PBMR using ceramic composite membranes. A comparison is given in Figure 5.12. It has to be noted that the pressure drop over the metal membrane is approximately one-third that of the ceramic membrane (Figure 5.12c). For this reason, the focus is set on those experiments with varying contact times because they demonstrate most sensitively the impact of trans-membrane pressure drop on reactor performance. In comparison to the PBMR experiments with the ceramic membrane for short contact times, that means at high feed ﬂow rates (W/F = 100 kg s/m3, see

153

5 Packed-Bed Membrane Reactors 80

(b)

Selectivity C2H4 [%]

Selectivity C2H4 [%]

(a) 70

60

50 PBMR: 100 FBR: 100 PBMR-SM: 100

40 0

20

PBMR: 200 FBR: 200 PBMR-SM: 200 40

(c)

80

70

60

50

40 480

60

530

580

630

680

Temperature [°C]

Conversion C2H6 [%] 2

Ceramic membrane

Δ pMembrane [bar]

154

Sinter metal membrane (PBMR-SM)

1.5

T=600°C

1

0.5

0 100

200

300

400

W/F [kgs/m³] Figure 5.12 Comparison of ﬁxed-bed (PBR) and one-stage membrane reactors using ceramic (PBMR) and sintered metal membranes (PBMR-SM). a) Ethylene selectivity versus conversion. b) Ethylene

selectivity versus temperature. xC2H6in = 1.5%, O2/CnHm = 1, W/F = 100–200 kg s/m3. c) Pressure drop over the ceramic and sintered metal membrane at 600 °C.

Figure 5.12a,b), the performance of the PBMR with the sintered metal membrane is slightly lower. Plotting ethylene selectivity versus ethane conversion also for higher contact times (W/F = 200 kg s/m3) as illustrated in Figure 5.12a, the pattern of PBMR-SM is between those of PBMR using ceramic membranes and PBR. This indicates that, due to the lower trans-membrane pressure drop shown in Figure 5.12c for the metal membrane, back-diffusion is expected to play a larger role than for the ceramic membrane. The problem of back-diffusion was investigated in detail and already discussed by (Tota et al., 2006, 2007). However, despite this limitation, the usage of metal membranes with their better characteristics regarding construction and mechanical stability is possible in principle and can be considered as an attractive alternative to overcome the problems with ceramic membranes if a sufﬁcient level of trans-membrane pressure drop can be reached.

5.5 Results for the Oxidative Dehydrogenation of Ethane to Ethylene (b)

(a)

Total flow rate [l/h]

Molar fraction O2 [%]

PBMR-3 10-30-60 PBMR-3 33-33-33 PBMR-3 60-30-10

Diff. selectivity C2H4 [%]

PBMR 1

PBMR 2 PBMR 3

O2 z/L

(c)

τ decreases

z/L

90

PBMR-3 10/30/60 PBMR-3 33/33/33 PBMR-3 60/30/10

80 70 60 50

PBMR 1

40

PBMR 2

PBMR 3

30 0

0.2

0.4

0.6

0.8

1

z/L Figure 5.13 Simulation results for: a) total ﬂow rate, b) molar fraction of oxygen, c) differential ethylene selectivity in a three-stage membrane reactor cascade. W/F = 400 kg s/m3, xC2H6in = 1.5%, xO2 = 0.75%, T = 600 °C.

5.5.4 Investigation of a Membrane Reactor Cascade – Impact of Dosing Proﬁles

A detailed proposition concerning the local reaction rates including undesired parallel–series reactions is given by the differential selectivity. For the postulated reaction network of the ODH of ethane to ethylene (Figure 5.3) the differential selectivity introduced in Chapter 1 (Equation 1.30) is deﬁned for the ODH of ethane as follows: Differential selectivity C2H4 =

r1 − r3 − r4 r1 + r2

(5.15)

Especially for the investigation of suitable dosing proﬁles inﬂuencing the local oxygen concentration and contact time in the three-stage membrane reactor cascade (PBMR-3) the differential selectivity is a useful parameter. In the PBMR-3 three different dosing proﬁles were investigated: increasing (10/30/60%), uniform (33/33/33%) and decreasing (60/30/10%). The resulting axial total ﬂow rates and axial molar fractions of oxygen are depicted in Figure 5.13a,b,

155

156

5 Packed-Bed Membrane Reactors

respectively. The increasing dosing proﬁle is characterized by a very low oxygen concentration, especially in the ﬁrst and second stages (Figure 5.13a). Based on the obtained local oxygen concentration the highest selectivity of the intermediate ethylene can be expected. Corresponding to the lowest total ﬂow rate as well as the highest residence times of the reactants can be obtained by realising an increasing dosing proﬁle. So a high ethane conversion can be expected as long as oxygen is available. Figure 5.13c illustrates the differential selectivity of ethylene, calculated by means of the reduced 1-D model, as a function of the dimensionless cascade length, ξ = Z/L. In general the differential selectivity decreases over the reactor length, based on the increasing intermediate concentration of ethylene and the resulting increasing reaction rates r3 and r4, respectively. For the chosen simulation conditions of long contact times and low oxygen concentration (W/F = 400 kg s/m3, xO2 = 0.75%) the increasing dosing proﬁle (10/30/60%) reveals the highest differential selectivity of ethylene. The increasing dosing proﬁle is characterized by a very low oxygen level, especially in the ﬁrst PBMR, corresponding to a long contact time. Thus, the desired reaction r1 forming ethylene can take place. Simultaneously, the ethyleneconsuming consecutive reactions r3 and r4 are suppressed due to the low oxygen level (see Figure 5.13a). In contrast, the uniform (33/33/63%) and decreasing (60/30/10%) dosing proﬁles are characterized by a higher local oxygen level. The obtained performance parameters of the experimentally investigated PBMR3 are given in Figure 5.14. Based on the kinetics and the reaction network the ethane conversion is increasing and selectivity of the desired intermediate product ethylene is decreasing with increasing temperature as discussed for the singlestage membrane reactor PBMR. The highest conversion (Figure 5.14a) can be obtained for the uniform and decreasing dosing proﬁles. The temperature-dependence of the ethane conversion is very similar for both. The increasing dosing proﬁle (10/30/60%) reveals a slightly lower conversion, due to oxygen limitation, especially for high temperatures. In general the membrane reactor cascade demonstrates a better performance with respect to conversion of ethane compared to the single-stage PBMR and the conventional ﬁxed-bed reactor. An explanation is the higher residence time of the reactants by means of distributed dosing, which is more signiﬁcant in the cascade. The integral ethylene selectivity of the cascade is illustrated in Figure 5.14b. As predicted in the calculations, the increasing dosing proﬁle shows the highest ethylene selectivity followed by the constant and decreasing proﬁles. Thus, the sequence of ethylene selectivity for a comparable conversion is shown in Figure 5.14c. Additionally, the selectivity of ethylene at the outlet of the particular stages (axial concentration proﬁle) for T = 600 °C is given in Figure 5.14d. It can be recognised that, at the outlet of the ﬁrst stage, the increasing dosing proﬁle shows a signiﬁcant enhancement of the intermediate selectivity. The corresponding low local concentration of oxygen is responsible for the suppression of further oxidation to CO and CO2, respectively. Due to the non-optimal condition that the total amount of dosed oxygen was taken the same in all reactor conﬁgurations, the rapid increase of local oxygen concentration, especially in the

5.5 Results for the Oxidative Dehydrogenation of Ethane to Ethylene

(b)

70

Selectivity C2H4 [%]

Conversion C2H6 [%]

(a)

PBMR 3 out

60

50

40

30

20 480

530

580

65

PBMR 3 out 60

55

50

45 480

630

Temperature [°C]

530

580

630

Temperature [°C] (d)

70

Selectivity C2H4 [%]

Selectivity C2H4 [%]

(c)

PBMR-3 10-30-60 PBMR-3 33-33-33 PBMR-3 60-30-10

60

50

O2

85

PBMR 1 out

75

T=600°C PBMR 2 out

65

PBMR 3 out

55

45

40 0

20

40

60

80

Conversion C2H6 [%] Figure 5.14 a) Conversion of ethane versus temperature, b) selectivity of ethylene versus temperature, c) selectivity of ethylene versus ethane conversion, d) selectivity of

50

150

250

350

450

W/F [kgs/m³] ethylene at the outlet of every single membrane reactor in the cascade. xC2H6in = 1.5%, O2/C2H6 = 1, W/F = 400 kg s/ m3.

third stage, impairs the ethylene selectivity due to undesired consecutive reactions. Nevertheless, the trend of an enhanced selectivity obtained by the increasing dosing proﬁle is obvious. 5.5.5 Quantitative Comparison of the Investigated Reactor Conﬁgurations

Table 5.3 gives a short summary with respect to performance parameters obtained from the experimental investigation of the ODH of ethane to ethylene using ceramic membranes in single-stage and multi-stage operation. It can be seen that a distributed dosing of oxygen via membranes leads to a signiﬁcant increase of the ethylene selectivity from 46.3% (PBR) to 52.3% (PBMR) applying a single-stage operation. Further improvement of reactor performance is possible using a multi-stage reactant dosing and applying an increasing dosing proﬁle. In particular the investigated increasing dosing proﬁle (PBMR-3; 10/30/60%) revealed an enhanced selectivity of ethylene and simultaneously a

157

158

5 Packed-Bed Membrane Reactors Table 5.3 Performance parameter of all investigated reactor conﬁgurations: T = 610 °C,

xC2H6in = 1.5%, O2/C2H6 = 1, W/F = 400 kg s/m3.

Conﬁguration PBR PBMRa) PBMR-3 10/30/60% PBMR-3 33/33/33% PBMR-3 60/30/10% a)

Conversion C2H6

Selectivity C2H4

Yield C2H4

Yield CO

Yield CO2

[%] 55.4 50.1 60.2 60.5 61.8

[%] 46.3 52.3 52.5 50.1 47.8

[%] 25.6 26.2 31.6 30.3 29.5

[%] 21.2 17.6 20.0 22.8 24.7

[%] 5.6 5.1 6.1 6.7 7.0

Ceramic membrane, γ Al2O3 10 nm.

higher ethane conversion. Thus, a maximal ethylene yield of 31.6% was observed in the PBMR-3 for the considered conditions (PBR 25.6%). The improved reactor performance is due to the favorable change of the local concentration and residence time proﬁles in the PBMR, which is more pronounced in a membrane reactor cascade.

5.6 Results for the Oxidative Dehydrogenation of Propane 5.6.1 Comparison Between PBR and a Single-Stage PBMR Using Ceramic Membranes

As a second and from the industrial point of view more interesting reaction, the oxidative dehydrogenation (ODH) of propane to propylene on the same VOx/γAl2O3 catalyst was investigated experimentally. For the propane system a detailed analysis of the reaction network was recently given by Liebner, 2003. Figure 5.15a,b compares the performance of a single-stage PBMR using a ceramic membrane and the conventional PBR in a pilot-scale for lean oxygen conditions (O2/C3H8 = 1), and Figure 5.15c,d does the same for excess oxygen conditions (O2/C3H8 = 4). In comparison to the ODH of ethane a similar trend with respect to the selectivity can be obtained (Figure 5.15). However, propylene selectivity depends stronger on temperature. Thus, the selectivity of propylene is decreasing strongly with increasing temperature as well as conversion, nearly independently from the investigated oxygen concentration. Nevertheless, under lean oxygen conditions (Figure 5.15a,b) and at high contact times, signiﬁcantly higher propylene selectivity was obtained. This trend is more pronounced for temperatures above 450 °C, where the inﬂuence of series reactions is stronger. The latter can be avoided by a distributed dosing via membranes. In contrast to the operation window at lean oxygen conditions the performance of PBMR and PBR is comparable for high

5.6 Results for the Oxidative Dehydrogenation of Propane 90 80

PBMR: 100

FBR: 100

PBMR: 400

FBR: 400

(b)

Selectivity C3H6 [%]

Selectivity C3H6 [%]

(a)

70 60 50 40 30

O2

20 10 0

5

10

15

20

25

90 80

60 50 40 30 20 10 0 325

30

Selectivity C3H6 [%]

80 70 60 50 40 30 20

O2

10 0 0

10

20

30

40

50

Conversion C3H8 [%]

O2

W/F 375

425

475

525

Temperature [°C]

60

(d)

80

Selectivity C3H6 [%]

Conversion C3H8 [%] (c)

W/F

70

70 60 50 40 30 20 10 0 350

O2 400

450

500

550

Temperature [°C]

Figure 5.15 a), c) Selectivity of propylene versus conversion. b), d) Selectivity of propylene versus temperature. xC3H8in = 1%, O2/C3H8 = 1O2↓ and 4O2↑, W/F = 100–400 kg s/m3.

contact times (W/F = 400 kg s/m3) and excess oxygen conditions. In this operation region the application of a PBMR is not favorable. In general the dosing concept via a PBMR is less efﬁcient than for the ODH of ethane discussed above. 5.6.2 Investigation of a Three-Stage Membrane Reactor Cascade

Figure 5.16 summarizes selected results of the experimental investigations of the cascade for the ODH of propane. Regarding propane conversion, depicted in Figure 5.16a, the results of all considered dosing proﬁles are close together. The dependency with respect to the local oxygen concentration inﬂuenced by the dosing proﬁle is even less pronounced than for the ODH of ethane. Nevertheless, an enhancement of the propylene selectivity of approximately 9% was obtained for the increasing dosing proﬁle (10/30/60%) at higher reaction temperatures (Figure 5.16b). Figure 5.16c gives the propylene selectivity along the three-stage membrane reactor cascade. In this case the increasing dosing proﬁle shows the highest selectivity along the whole cascade length. Due to the less pronounced sensitivity with respect to oxygen, compared to the ODH of ethane the strong increase of

159

5 Packed-Bed Membrane Reactors (b)

Selectivity C3H6 [%]

Conversion C3H8 [%]

(a) 40 PBMR 3 out

30

20

10

0 325

375

425

475

(c)

70

PBMR 1 out

70

PBMR-3 10-30-60 PBMR-3 33-33-33 PBMR-3 60-30-10

60

50

40

30

20 325

525

Temperature [°C]

Selectivity C3H6[%]

160

PBMR 2 out

375

425

475

525

Temperature [°C]

T=600°C

60

PBMR 2 out

50

PBMR 3 out

40

30

20 50

150

250

350

450

WHSV [kg.s/m³] Figure 5.16 a) Propane conversion versus temperature, b) propylene selectivity versus temperature, c) propylene selectivity at the outlet of every single membrane reactor in the cascade. xC3H8in = 1%, O2/C3H8 = 1, W/F = 400 kg s/m3.

local concentration in the third stage does not affect overall propylene selectivity signiﬁcantly.

5.7 Summary and Conclusions

Based on an optimal distributed dosing of reactants and the resulting concentration and residence time effects, the product spectrum can differ signiﬁcantly in a packed-bed membrane reactor compared to a conventional ﬁxed-bed reactor. A detailed experimental investigation of single- and multi-stage membrane reactors as well as a conventional ﬁxed-bed reactor concept was carried out in a pilotscale reactor set-up, allowing the experimental validation of theoretical results. At low oxygen concentrations the experiments using ceramic membranes in a single-stage PBMR indicate that the selectivity of the desired product ethylene can be increased signiﬁcantly for simultaneously high ethane conversions compared to a conventional ﬁxed-bed reactor (PBR: 46.3%; PBMR: 52.3%). Experiments carried out using sintered metal membranes revealed a comparable performance for high trans-membrane ﬂuxes. Due to the back-diffusion of reactants in the

Special Notation not Mentioned in Chapter 2

study, the more promising operating region, at higher contact times and lean oxygen conditions, could not be realized with these membranes. In this case a more favorable relation between catalyst activity and membrane permeability (i.e., more active catalyst) would be beneﬁcial. The application of a multi-stage dosing concept, by means of an increasing oxygen dosing proﬁle, reveals a pronounced increase of ethane conversion as a result of the higher residence time of the reactants for the conditions investigated. Thus, a maximal ethylene yield of 31.6% was observed in the membrane reactor cascade, in comparison to the yield of 25.6% in the reference concept (PBR). The improved reactor performance is due to the favorable change of the local concentration and residence time proﬁles by a distributed dosing, which is signiﬁcantly more pronounced in a membrane reactor cascade. The obtained results for the ODH of propane are comparable to those of the ODH of ethane, even though the increase in propylene selectivity is not so pronounced as in the case of ethylene. Propylene yield could be further enhanced using a multi-stage reactant feeding with an increasing dosing proﬁle. For the mathematical description of a packed-bed membrane reactor, models of different complexity were applied. Even a relatively simple 1-D pseudo-homogeneous model was able to reﬂect the main tendencies in reactor behavior. However, resulting from the simplifying assumptions made, more accurate predictions can be achieved only at high trans-membrane ﬂow rates and oxygen excess conditions. The main difference compared to the detailed 2-D model is neglected radial local oxygen distribution applying the 1-D model. Thus, the predicted ethane conversions overestimate the obtained experimental data. Especially for high contact times, bothethane conversion and ethylene selectivity could be described in a very good agreement with the detailed “λ(r) model” taking account of the radial oxygen concentration proﬁle and radial porosity distribution of the catalyst bed. The results of the performed theoretical analysis of PBMR and PBR revealed optimal operation conditions for the PBMR, that is, a maximum ethane conversion and ethylene selectivity, respectively, at higher residence times and at lean oxygen concentration. Future work should be devoted to further improve the compatibility between membrane and reaction as well as catalyst to exploit even better the potential of a distributed dosing of reactants in order to compensate the higher investment costs of the membrane reactor. Hereby potential is seen in particular in the application of sintered metal membranes.

Special Notation not Mentioned in Chapter 2 Latin Notation

A BC FT NR

m2 m3/s

cross-sectional area boundary condition total volumetric ﬂow rate number of reactions

161

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5 Packed-Bed Membrane Reactors

s S C2H 4 Sdiff TS/SS VR W/F Z

stage number in the cascade total number of stages differential selectivity of ethylene m3 kg s/m3 m

ratio of tube side to shell side reactor volume weight of catalyst/total ﬂow rate total length of the cascade

Greek Notation

ξ

Dimensionless length

References Al-Juaied, M.A., Lafarga, D., and Varma, A. (2001) Ethylene epoxidation in a catalytic packed-bed membrane reactor: experiments and model. Chem. Eng. Sci., 56, 2. Alonso, M., Lorences, M.J., Pina, M.P., and Patience, G.S. (2001) Butane partial oxidation in an externally ﬂuidized bed-membrane reactor. Catal. Today, 67, 151–157. Bey, O. (1998) Strömungsverteilung und Wärmetransport, Universität Stuttgart, Dissertation. Caro, J. (2006) Membranreaktoren für die katalytische Oxidation. Chem. Ing. Tech., 78, 899–912. Caro, J., Schiestel, T., Werth, S., Wang, H., Kleinert, A., and Kölsch, P. (2006) Perovskite hollow ﬁbre membranes in the partial oxidation of methane to synthesis gas in a membrane reactor. Desalination, 199, 415–417. Cheng, P., and Vortmeyer, D. (1988) Transverse thermal dispersion and wall channeling in a packed-bed with forced convective ﬂow. Chem. Eng. Sci., 43, 9. COMSOL (2006) Handbook, Comsol Multiphysics 3.2, 1997–2007 COMSOL, Inc. Coronas, J., Menendez, M., and Santamaria, J. (1995) Use of a ceramic membrane reactor for the oxidative dehydrogenation of ethane to ethylene and higher hydrocarbons. Ind. Eng. Chem. Res., 34, 12.

Diakov, V., Lafarga, D., and Varma, A. (2001) Methanol oxidative dehydrogenation in a catalytic packed-bed membrane reactor. Catal. Today, 67, 1–3. Diakov, V., and Varma, A. (2004) Optimal feed distribution in a packed-bed membrane reactor: the case of methanol oxidative dehydrogenation. Ind. Eng. Chem. Res., 43, 309–314. Edgar, T.F., and Himmelblau, D.M. (1988) Optimization of Chemical Processes, McGraw-Hill Education, ISBN: 0070189927. Ergun, S. (1952) Fluid ﬂow through packed columns. Chem. Eng. Prog., 35, 89–94. Farrusseng, D., Julbe, A., and Guizard, C. (2001) Evaluation of porous ceramic membranes as O2 distributors for the partial oxidation of alkanes in inert membrane reactors. Sep. Purif. Technol., 25, 137–149. Grabowski, R. (2006) Kinetics of oxidative dehydrogenation of C2-C3 alkanes on oxide catalysts. Catal. Rev., 48, 199–268. Hamel, C., Thomas, S., Schädlich, K., and Seidel-Morgenstern, A. (2003) Theoretical analysis of reactant dosing concepts to perform parallel-series reactions. Chem. Eng. Sci., 58, 4483–4492. Hamel, C., Seidel-Morgenstern, A., Schiestel, T., Werth, S., Wang, H., Tablet, C., and Caro, J. (2006) Experimental and modeling study of the O2-enrichment by perovskite ﬁbers. AIChE J., 52, 3118– 3125.

References Hein, S. (1999) Modellierung wandgekühlter katalytischer Festbettreaktoren mit Ein- und Zweiphasenmodellen, VDI-Verlag, Düsseldorf, ISBN: 3-18-359303-3, Dissertation, München. Hodnett, B.K. (2000) Heterogeneous Catalytic Oxidation : Fundamental and Technological Aspects of the Selective and Total Oxidation of Organic Compounds, John Wiley and Sons (Asia) Pte Ltd, ISBN: 0-471-48994-8. Hunt, M.L., and Tien, C.L. (1990) Nondarcian ﬂow, heat and mass-transfer in catalytic packed-bed reactors. Chem. Eng. Sci., 45, 1. Hussain, A. (2006) Heat and mass transfer in tubular inorganic membranes, Magdeburg, Dissertation. Hussain, A., Seidel-Morgenstern, A., and Tsotsas, E. (2006) Heat and mass transfer in tubular ceramic membranes for membrane reactors. Int. J. Heat Mass Transf., 49, 2239–2253. Joshi, M. (2007) Statistical analysis of models and parameters in chemical and biochemical reaction networks, Otto von Guericke University Magdeburg, Dissertation. Klose, F., Wolff, T., Hamel, C., Alandjiyska, M., Weiß, H., Joschi, M., Tota, A., and Seidel-Morgenstern, A. (2003a) Partial oxidation of ethane- the potential of membrane reactors. J. Univ. Chem. Technol. Metall., 38, 25–40. Klose, F., Wolff, T., Thomas, S., and Seidel-Morgenstern, A. (2003b) Concentration and residence time effects in packed bed membrane reactors. Catal. Today, 82, 1–4. Klose, F., Joshi, M., Hamel, C., and Seidel-Morgenstern, A. (2004a) Selective oxidation of ethane over a VOx/Al2O3 catalyst investigation of the reaction network. Appl. Catal. A Gen., 260, 101–110. Klose, F., Joshi, M., Hamel, C., and Seidel-Morgenstern, A. (2004b) Selective oxidation of ethane over a VOx/gammaAl2O3 catalyst—investigation of the reaction network. Appl. Catal. A Gen., 260, 1. Kölsch, P., Noack, M., Schäfer, R., Georgi, G., Omorjan, R., and Caro, J. (2002) Development of a membrane reactor for the partial oxidation of hydrocarbons:

direct oxidation of propane to acrolein. J. Membr. Sci., 198, 119–128. Kürten, U., van Sint Annaland, M., and Kuipers, J.A.M. (2004) Oxygen distribution in packed-bed membrane reactors for partial oxidations: effect of the radial porosity proﬁles on the product selectivity. Ind. Eng. Chem. Res., 43, 1823–1835. Lafarga, D., Santamaria, J., and Menéndez, M. (1994) Methane oxidative coupling using porous ceramic membrane reactors – I. reactor development. Chem. Eng. Sci., 49, 2005–2013. Levenspiel, O. (1999) Chemical Reaction Engineering, John Wiley & Sons Inc. Liebner, C. (2003) Einführung der Polythermen Temperatur Rampen Methode für die Ermittlung kinetischer Daten, Universität Berlin, Dissertation. Liebner, C., Wolf, D., Baerns, M., Kolkowski, M., and Keil, F.J. (2003) A high-speed method for obtaining kinetic data for exothermic or endothermic catalytic reactions under nonisothermal conditions illustrated for the ammonia synthesis. Appl. Catal. A Gen., 240, 95–110. Lu, Y.P., Dixon, A.G., Moser, W.R., and Ma, Y.H. (1997a) Analysis and optimization of cross-ﬂow reactors for oxidative coupling of methane. Ind. Eng. Chem. Res., 36, 3. Lu, Y.P., Dixon, A.G., Moser, W.R., and Ma, Y.H. (1997b) Analysis and optimization of cross-ﬂow reactors with distributed reactant feed and product removal. Catal. Today, 35, 4. Lu, Y.P., Dixon, A.G., Moser, W.R., and Ma, Y.H. (1997c) Analysis and optimization of cross-ﬂow reactors with staged feed policies = isothermal operation with parallel series, irreversible reaction systems. Chem. Eng. Sci., 52, 8. Lu, Y., Dixon, A.G., Moser, W.R., and Ma, Y.H. (2000) Oxidative coupling of methane in a modiﬁed g-alumina membrane reactor. Chem. Eng. Sci., 55, 4901–4912. Mallada, R., Menéndez, M., and Santamaría, J. (2000a) Use of membrane reactors for the oxidation of butane to maleic anhydride under high butane concentrations. Catal. Today, 56, 191–197.

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5 Packed-Bed Membrane Reactors Mallada, R., Pedernera, M., Menendez, N., and Santamaria, J. (2000b) Synthesis of maleic anhydride in an inert membrane reactor. Effect of reactor conﬁguration. Ind. Eng. Chem. Res., 39, 3. Mason, E.A., and Malinauskas, A.P. (1983) Gas Transport in Porous Media: The Dusty-Gas Model, Elsevier, Amsterdam, ISBN: 0-444-42190-4. Morbidelli, M., Gavriilidis, A., and Varma, A. (2001) Catalyst Design: Optimal Distribution of Catalyst in Pellets, Reactors and Membranes, Cambridge University Press Cambridge. Ramos, R., Menendez, M., and Santamaria, J. (2000) Oxidative dehydrogenation of propane in an inert membrane reactor. Catal. Today, 56, 1–3. Schäfer, R., Noack, M., Kolsch, P., Stohr, M., and Caro, J. (2003) Comparison of different catalysts in the membranesupported dehydrogenation of propane. Catal. Today, 82, 1–4. Seidel-Morgenstern, A. (2005) Analysis and Experimental Investigation of Catalytic Membrane Reactors, in Integrated Chemical Processes : Synthesis, Operation, Analysis, and Control, Wiley-VCH Verlag GmbH, Weinheim, ISBN: 3-527-30831-8. Sheldon, R.A., and van Santen, R.A. (1995) Catalytic Oxidation: Principles and Applications -A Course of the Netherlands Institute for Catalysis Research, World Scientiﬁc Publishing, Catalysis Research. Tellez, C., Menendez, M., and Santamaria, J. (1997) Oxidative dehydrogenation of butane using membrane reactors. AIChE J., 43, 3. Thomas, S. (2003) Kontrollierte Eduktzufuhr in Membranreaktoren zur Optimierung der Ausbeute gewünschter Produkte in Parallel- und Folgereaktionen, Dissertation. Thomas, S., Klose, F., and Seidel-Morgenstern, A. (2001) Investigation of mass transfer through inorganic membranes with several layers. Catal. Today, 67, 205–216. Tonkovich, A.L.Y., Jimenez, D.M., Zilka, J.L., and Roberts, G.L. (1996a) Inorganic membrane reactors for the oxidative coupling of methane. Chem. Eng. Sci., 51, 11.

Tonkovich, A.L.Y., Zilka, J.L., Jimenez, D.M., Roberts, G.L., and Cox, J.L. (1996b) Experimental investigations of inorganic membrane reactors: a distributed feed approach for partial oxidation reactions. Chem. Eng. Sci., 51, 789–806. Tota, A., Hamel, C., Thomas, S., Joshi, S., Klose, F., and Seidel-Morgenstern, A. (2004) Theoretical and experimental investigation of concentration and contact time in membrane reactors. Chem. Eng. Res. Des., 82, 236–244. Tota, A., Hamel, C., Klose, F., Tsotsas, E., and Seidel-Morgenstern, A. (2006) Enhancement of intermediate product selectivity in multi-stage reactors-Potential and Pitfalls, ISCRE 19, Potsdam, Poster 275. Tota, A., Hlushkou, D., Tsotsas, E., and Seidel-Morgenstern, A. (2007) Packed Bed Membrane Reactors, in Modelling of Process Intensiﬁcation (Herausgeber: ed. F. Keil), Wiley-VCH Verlag GmbH, Weinheim, ISBN: 3-527-31143-2 99, pp. 99–149. Tsotsas, E. (2002) VDI-Wärmeatlas, Springer, Berlin, p. 1366. Tsotsas, E., and Schlünder, E.-U. (1990) Heat transfer in packed beds with ﬂuid ﬂow: remarks on the meaning and the calculation of a heat transfer coefﬁcient at the wall. Chem. Eng. Sci., 45, 4. Wang, H., Tablet, C., Schiestel, T., and Caro, J. (2006) Hollow ﬁber membrane reactors for the oxidative activation of ethane. Catal. Today, 118, 98–103. Westerterp, K.R., van Swaaij, W.P.M., and Beenackers, A.A.C.M. (1984) Chemical Reactor Design and Operation, John Wiley & Sons, Ltd, ISBN: 0471901830. Winterberg, M., and Tsotsas, E. (2000a) Correlations for effective heat transport coefﬁcients in beds packed with cylindrical particles. Chem. Eng. Sci., 55, 23. Winterberg, M., and Tsotsas, E. (2000b) Impact of tube-to-particle-diameter ratio on pressure drop in packed beds. AIChE J., 46, 5. Winterberg, M., Tsotsas, E., Krischke, A., and Vortmeyer, D. (2000) A simple and coherent set of coefﬁcients for modelling of heat and mass transport with and without chemical reaction in tubes ﬁlled with spheres. Chem. Eng. Sci., 55, 5.

References Zeng, Y., Lin, Y.S., and Swartz, S.L. (1998) Perovskite-type ceramic membrane: synthesis, oxygen permeation and membrane reactor performance for oxidative coupling of methane. J. Membr. Sci., 150, 87–98.

Ziaka, Z.D., Minet, R.G., and Tsotsis, T.T. (1993) Propane dehydrogenation in a packed-bed membrane reactor. AIChE J., 39, 3.

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6 Fluidized-Bed Membrane Reactors Desislava Tóta, Ákos Tóta, Stefan Heinrich, and Lothar Mörl

6.1 Introduction

Many membrane reactor applications, which lead to higher educt conversion and yields of intermediates, are related to packed-bed conﬁgurations (Marcano and Tsotsis, 2002; Saracco et al., 1999; Dixon, 2003). However, packed-bed membrane reactors (PBMR) also possess the disadvantage of large temperature gradients for highly exothermic reactions, which may lead to catalyst coking, further undesirable side reactions and reactor instability. These disadvantages can be largely overcome by integrating the membranes inside a ﬂuidized bed, referred to as a ﬂuidized-bed membrane reactor (FLBMR). A FLBMR is a special type of reactor that combines the advantages of a ﬂuidized bed and a membrane reactor. One of the main advantages of the ﬂuidizedbed reactor (FLBR) is the excellent tube-to-bed heat transfer, which allows a safe and efﬁcient reactor operation even for highly exothermic reactions. The intense macro-scale solids mixing induced by the rising bubbles results in a remarkable temperature uniformity, even in beds as large as 10 m (Miracca and Capone, 2001). Other advantages of FLBRs are low pressure drop and the potential to control the catalyst activity due to continuous processing, for example, catalyst regeneration in circulating ﬂuidized beds. There are a few drawbacks compared to the ﬁxed-bed reactors – gas back-mixing, bypassing and erosion of reactor internals and catalyst attrition – which can hinder the development of the ﬂuid-bed technology. By the insertion of membranes in a ﬂuidized bed a synergistic effect can be accomplished. First, optimal concentration proﬁles can be created via controlled dosing or withdrawal; and second, the ﬂuidization behavior can be improved via the presence of inserts and permeation of the gas through the membranes, so that large improvements in conversion and selectivity might be achieved. Some ﬁrst concepts of ﬂuidized-bed reactors with controlled reactant distribution used nozzles for secondary gas injection. Mleczko et al. (1994) investigated the oxidative coupling of methane to C2+ hydrocarbons. To improve the mass transfer by reduced bubble size, the oxygen was injected via secondary distributor Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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in the ﬂuidized bed. The product selectivity and yield were increased in part of the operation range. A signiﬁcant inﬂuence of the secondary gas injections was approved. A concept for separate reactant dosing was proven by Soler et al. (1999) for the oxidative dehydrogenation of n-butane to butadiene by separation of the oxidation and the reduction zones in the same catalytic ﬂuidized bed. The butadiene yield was about 200% higher than in the conventional reactor. Al-Sherehy, Grace, and Adris (2005) investigated the effect of the discrete distributing gaseous feed along a bubbling ﬂuidized bed on the ethane partial oxidation to ethylene and acetic acid. An improvement of the product selectivity and the reactor performance was achieved by using multiple nozzles for the secondary gas injection. Recent developments in the material sciences, and especially the development of suitable inorganic membranes which are chemically resistant and stable at high temperatures, offer the integration of membranes into catalytic reactors and a new reactor design. Only a limited number of applications of the membrane-assisted FLBR for the distributive feeding of one of the reactants have been investigated and most of these applications involve the controlled dosing of reactant via porous membranes. Alonso et al. (2001) studied the butane partial oxidation in an externally FLBMR. Air from a pre-heated ﬂuidized bed (catalytic inert) ﬂows across a catalyst-ﬁlled membrane tube. A detailed reactor model demonstrated a minimized hot spot effect and maleic anhydride yields were predicted to be 50% higher compared to a conventional ﬁxed-bed reactor. However, later experimental data (Alonso et al., 2005) show that, on average, the overall performance in the conventional ﬁxed bed is superior to the membrane conﬁguration because selectivity is higher and the reactor may be operated at higher temperatures resulting in superior MA yields. Ramos et al. (2001) proposed a similar concept for the partial oxidation of propane to propene. Air ﬂuidized the shell side where catalyst-ﬁlled membrane tubes and cooling coils were immersed. Oxygen transport through the membrane was controlled by the pressure drop. The controlled oxygen addition along the axis improved the propene selectivity and broadened the operating range with respect to the hydrocarbon and oxygen feed rates. Recently, Deshmukh et al. (2005a, 2005b) constructed a small laboratory-scale FLBMR for the partial oxidation of methanol to formaldehyde. High methanol conversion and high selectivity to formaldehyde were achieved with safe reactor operation (isothermal reactor conditions) at higher methanol inlet concentrations than that currently employed in industrial processes. An area of much current interest is the production of hydrogen via methane steam reforming or autothermal reforming. Fluidized-bed concepts were proposed to solve the problems of thermal control encountered in ﬁxed-bed reactors. These studies showed that, for steam reforming of natural gas, the thermodynamic equilibrium restrictions can be overcome by in situ separation and removal of hydrogen via perm-selective thin-walled palladium-based membranes, leading to

6.1 Introduction

B

C, D

Tubular sinter metal membranes

A Figure 6.1

Schematic of the dosing concept of the FLBMR.

increased synthesis gas yields in comparison to the industrial ﬁxed-bed steam reformer (Chen, Yan, and Elnashaie, 2003; Patil, Annaland, and Kuipers, 2005; Adris, Lim, and Grace, 1997). This short overview demonstrates the wide ﬁeld of applications and the crucial role of the reaction system. A more comprehensive review on the potential and hurdles of FLBMRs is given by Deshmukh et al. (2007). The present chapter studies experimental and theoretical analysis of the potential of the FLBMR concept (continuous distributed reactant dosing) for the same reaction as introduced in Chapter 3, that is, the oxidative dehydrogenation of ethane to ethylene on a VOx/γ-Al2O3 catalyst in comparison to a FLBR with co-feed reactant. In the FLBMR concept one of the reactant (oxygen) was distributed via vertically inserted tubular membranes in a bubbling FLBR of catalysts (Figure 6.1). The performance of the reactor was investigated in comparison to the conventional FLBR under various experimental conditions. This chapter gives an overview of the FLBMR by theoretical and experimental study. The next section presents a developed phenomenological reactor model and simulation results which illustrate the inﬂuence of some model parameters and attractive ranges for the new reactor concept. In the second part, experimental results demonstrate the beneﬁts and limitations of this reactor concept compared to co-feed reactant dosing in a conventional FLBR.

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6.2 Modeling of the Distributed Reactant Dosage in Fluidized Beds 6.2.1 Theory

A theoretical study has been carried out to describe the effects of segregated reactant dosage on the reactor performance in ﬂuidized beds and to identify attractive parameter ranges for reactor operation. Due to the complex ﬂuid dynamics of the ﬂuidized bed, in this work a phenomenological model was applied. It is well known for a ﬂuidized bed that bubbles, particle cluster and clouds greatly inﬂuences the reactor performance. Their characteristics can be changed by internals (Jin, Wei, and Wang, 2003) or by secondary gas injection (Al-Sherehy, Grace, and Adris, 2004; Deshmukh, 2004; Christensen, Coppens, and Nijenhuis, 2005). Therefore, this simulation study should show the uncertainties and limits of phenomenological models of the FLBMR. A heterogeneous two-phase model has been derived and numerically solved for the simulation of the co-feed dosage and of the distributed reactant dosage in ﬂuidized beds via vertically installed membranes. The model describes the advectivedispersive mass transfer in the suspension and bubble phases, using effective dispersion coefﬁcients (dispersion model). By means of a schematic representation, the main features, notation and assumptions of the model are depicted in Figure 6.2. Important assumptions and features of the model are:

• • •

Steady-state one-dimensional reactor model.

• • •

Convective–dispersive mass transfer in the suspension phase.

Ideal gas behavior. Distinction between a particle-free bubble phase and a suspension phase with particles; consideration of mass transfer at the phase interface.

Plug ﬂow in the bubble phase. The chemical reaction takes place in the suspension phase. Concentration gradients inside the catalyst as well as between catalyst surface and suspension gas are neglected.

•

The change of the superﬁcial gas velocity due to the gas supply versus the bed height and the change of the mole fraction due to the reaction are considered.

•

The secondary gas can be fed to the bubble phase or distributed between the suspension gas and the bubble phase according to their fractions.

•

The suspension gas velocity is constant. Therefore, a unilateral convective mass ﬂow rate is deﬁned.

•

Reactions in the freeboard region are neglected.

6.2 Modeling of the Distributed Reactant Dosage in Fluidized Beds

Figure 6.2

Scheme of the two-phase ﬂuidized-bed model.

The resulting mass balances for the suspension and bubble phase are given in Equations 6.1–6.10. In order to describe the mass balances of both phases by means of second-order differential equations an axial dispersion coefﬁcient has been deﬁned for the balances of the bubble phase. The introduction of this “artiﬁcial” diffusion term serves solely numerical purposes. Therefore, the axial dispersion coefﬁcient has been set to a very low value of 10−5–10−6 m2/s. The rate of the reactions considered leading to the component speciﬁc source terms Ri are described in detail in Chapter 3.

•

Mass balance of a component i in the suspension phase: ∂ω s ,i ρs us (1 − ε b ) ∂ s dω s ,i ρs ⎤ = − ⎡(1 − ε b )Dax + ρCat (1 − ε s ) (1 − ε b ) MiRi + ,i ∂z ∂z ⎢⎣ dz ⎥⎦ (1 − ε b ) m m − kbs ,i a (ω s ,i ρs − ω b ,i ρb ) − K Q ρQ ,i (6.1) Lm Aapp

•

Mass balance of a component i in the bubble phase: ∂ ω b ,i ρ b u b ε b ∂ ε m b dω b ,i ρb ⎤ + b m + = − ⎡(1 − ε b )Dax ,i ∂z ∂z ⎣⎢ dz ⎦⎥ Lm Aapp kbs ,i a (ω s ,i ρs − ω b ,i ρb ) + K Q ρQ ,i

(6.2)

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6 Fluidized-Bed Membrane Reactors

•

Total mass balance of the bubble phase: ∂ ( ρb u b ε b ) ε m = ∑ [kbs ,i a (ω s ,i ρs − ω b ,i ρb )] + b m + K Q ρQ ∂z Lm Aapp i

(6.3)

The superﬁcial gas velocity u is obtained solving the continuity Equation 6.4.

•

Total mass balance:

ρuAapp = ρs us (1 − ε b ) Aapp + ρbub ε b Aapp

(6.4)

The superﬁcial gas velocity changes due to: (a) the gas supply over the bed height and (b) the chemical reaction. Therefore, a convective mass ﬂow is considered to keep the suspension gas velocity constant. In order to estimate the mass transfer coefﬁcient, the total mass ﬂow rate in the differential volume element dV of the suspension phase must be balanced:

(1 − ε b ) m m dm s dz = −K Q ρQ dV − ∑ [kbs ,i a (ω s ,i ρs − ω b ,i ρb )]dV + dz, dz Lm i

(6.5)

with V˙Q = KQρQdV as the volume ﬂow, which is transferred into the bubble or suspension phase. From the ideal gas law follows: m pVs = s RT Ms

(6.6)

dm s dV dρ = ρs s + Vs s dz dz dz

(6.7)

The gas volume ﬂow in the suspension phase is: Vs = us (1 − ε b ) Aapp

(6.8)

or rather: dVs dε = − Aappus b dz dz

(6.9)

By inserting Equations 6.9 and 6.7 in Equation 6.5, the mass transfer coefﬁcient can be calculated from: K Q ρQ = ρs us

(1 − ε b ) m m dε b dρ − us (1 − ε b ) s − ∑ [kbs ,i a (ω s ,i ρs − ω b ,i ρb )] + dz dz Lm Aapp i (6.10)

The ﬁrst two terms in Equation 6.10 describe mass ﬂow rate induced by the change of the local gradients of the bubble volume fraction and the suspension gas density. The convective mass transfer between the phases is expressed by the summand, while the last term describes the mass ﬂow of the component, which is distributed via the membranes. The composition of the above-deﬁned convective stream is affected by the suspension phase. When the mass transfer coefﬁcient KQ is positive, the density ρQ is equal to the density of the suspension phase ρs. If the calculated mass transfer

6.2 Modeling of the Distributed Reactant Dosage in Fluidized Beds Table 6.1

Boundary conditions for the two-phase ﬂuidized-bed reactor model.

At z = 0 ﬂux density

At z = Hbed convective ﬂux

( ∂∂ωz ) ∂ω (ω u ) = − D ( ∂z )

(ωb,i ub )0 = − Db,i s 0

s ,i

∂ωb,i =0 ∂z

+ ωs ,iou s

∂ωS ,i =0 ∂z

z =0

s ,i

s ,i

+ ωb,i 0ub

b ,i

z =0

coefﬁcient KQ is negative, the convective mass transfer occurs from the bubble phase to the suspension phase and has the composition of the bubble phase. For the solution of aforementioned second-order differential equation system, two boundary conditions must be deﬁned. Modeling both of the reactors as a closed system, Dankwert’s boundary condition at inlet and outlet are deﬁned (Table 6.1). The overall mass continuity equation for calculation of the local gas velocities can be obtained by summing up the individual component balances in the several phases. The resulting system of ordinary differential equations is solved simultaneously to the component balance equations. For the solution of the coupled differential equation system, the commercial simulation tool Femlab® 3.1 (Comsol AB, Stockholm) was used. With this package, the differential equation system was discretized by means of the ﬁnite element method. The resulting ordinary nonlinear equation system was solved using a UMFPACK algorithmus at each Newton iteration step. In phenomenological models of ﬂuidized-bed reactors, parameters like bubble diameter and bed porosity have to be considered, which again depend on the ﬂuid dynamics at the particular operation point. The hydrodynamic quantities needed were calculated using empirical or semi-empirical approximations (Table 6.2). 6.2.2 Parametric Sensitivity of the Model 6.2.2.1 Bubble Size By the use of membranes in a ﬂuidized bed optimal concentration proﬁles can be realized via controlled dosing; further the ﬂuidization behavior can be improved via internals and secondary gas permeation through the membranes. Internals in a ﬂuidized bed reduce the reactor equivalent diameter and the bubble size; therefore, conversion can be increased by better gas–solid mass transfer (Volk, Johnson, and Stotler, 1962; Kunii and Levenspiel, 1992). Kleijn van Willigen et al. (2005) found a signiﬁcant decrease in the bubble size and bubble hold-up due to the distributed secondary gas supply. Different investigations in ﬂuidized beds show a lower effective axial dispersion by means of the installation of tubular membranes (Deshmukh, 2004) or by the injection of secondary gas (Al-Sherehy, Grace, and Adris, 2004; Deshmukh, 2004; Christensen, Coppens, and Nijenhuis, 2005). This results in ﬂuid dynamics with plug ﬂow characteristics.

173

174

6 Fluidized-Bed Membrane Reactors Table 6.2 Parameters used in the model.

Mass transfer coefﬁcient between bubble and suspension phase (Werther and Schössler, 1999)

ksbab =

g 0.25 ⎤ 6ε b ⎡ umf + 0.95 ( Dmiε mf )0.5⎛⎜ ⎞⎟ ⎥ ⎢ ⎝ dv ⎠ ⎦ dv ⎣ 3

( )

Bubble size equation (Hilligardt, 1986)

d (dv ) 2ε b = 9π dz

Bubble phase fraction

ν rel(u − umf ) , where: ub H ν rel = 0.67 for bed ≤ 1.7, or : dapp

13

−

dv umf ⎞ ⎛ 3 ⎜ 280 ⎟ ub ⎝ g ⎠

(6.12)

εb =

ν rel = 0..51

H bed H for 1.7 ≤ bed ≤ 4.0 dapp dapp

(6.13)

Bubble rise velocity (Hilligardt and Werther, 1986)

ub = ν rel (u − umf ) + 0.71⋅δ g ⋅ dv , where δ = 3.2Da0 ,33

Axial dispersion coefﬁcient (Lee and Kim, 1989)

Pea =

Binary diffusion coefﬁcient by Fuller et al. (Poling, Prausnitz, and O’Connell, 2001) Multi-component diffusion coefﬁcient by Wilke (Poling et al., 2001)

(6.11)

Dij =

u 0Da ⎛ u0 ⎞ = 0.02566 ⎜ ⎝ umf ⎟⎠ D

−0.54

1 ⎞ ⎛ 1 + 0.01013T 1.75⎜ ⎝ Mi M j ⎟⎠

Dim =

1 − yi i Dij

∑y

0.067

( ) dp D

−0.588

(6.15)

0.5

P ⎡⎣(∑ υi ) + (∑ υ j ) ⎤⎦ 13

⎛ ρp ⎞ ⎜⎝ ρ ⎟⎠ g

(6.14)

13 2

(6.16)

(6.17)

j j ≠1

Despite intensive research, there were no correlations to describe back-mixing and bubble growth in ﬂuidized beds with internals and secondary gas injection. Thus, in our model, the calculation of the size and rise velocity of the bubbles is based on empirical correlations obtained in ﬂuidized beds without internals and without secondary gas injection. In order to evaluate the sensitivity of the simulation results regarding bubble size, the empirical correlation for the bubble growth rate (6.12) was modiﬁed by multiplying the calculated values with a factor Kdv. Since the aforementioned studies report small bubbles in ﬂuidized beds with internals and secondary gas injection, the factor Kdv was varied between 0.1 and 1.2. All hydrodynamic quantities were calculated according to the correlations given in Table 6.2. Figure 6.3 shows the results for oxygen concentrations at 1 and 5 vol% at a secondary to primary gas ﬂow ratio of Fs/Fp = 1. The simulation results can be interpreted as mass transfer limitations between the bubble and the suspension phase due to the decrease of the total bubble surface area with increasing bubble size. Additionally, the larger bubbles rise faster over

6.2 Modeling of the Distributed Reactant Dosage in Fluidized Beds

Figure 6.3 Variation of the bubble diameter in the FLBMR: c(C2H6) = 1 vol%, u = 0.3 m/s, mCat/F = 1000 kg·s/m3, Fs/Fp = 1.0, T = 590 °C.

the bed and have a shorter contact time. Assuming that the reaction takes place only in the suspension phase, the ethane conversion decreases, because a large fraction of the reactants is captured in the bubble phase. An important fact is that ethane conversion is more sensitive than ethylene selectivity concerning this factor. In particular, this is pronounced in the range of low O2 concentrations, which is characterized by low driving forces in the suspension phase, resulting in limitations of the reaction rate. It must be pointed out that the ethane is fed at the reactor inlet (i.e., in both phases), whereas the oxygen is transferred into the suspension phase only via the bubbles. A small amount of co-fed oxygen could therefore improve the ethane conversion. For a detailed analysis of bubble growth in the FLBMR, further experimental studies are necessary in order to describe the effects of reactor geometry and gas supply on the hydrodynamics. Recently, in silico measurements, based on more sophisticated modeling approaches like, for example, the discrete particle method or the Lattice–Boltzmann method are considered to ﬁll the lack of reliable correlations (Bokkers et al., 2006). 6.2.2.2 Secondary Gas Distribution There are different assumptions about the mechanism of the secondary gas distribution in a ﬂuidized bed. Christensen, Coppens, and Nijenhuis (2005) found that the secondary injection reduces bubble size and bubble fraction. Deshmukh et al. (2005a, 2005b) consider that the secondary gas is distributed between the bubble and suspension gases, although they could not ﬁnd clear evidence for this hypothesis in their experiments. A hydrodynamic investigation of the distribution of increased gas volume due to reaction (Adris, Lim, and Grace, 1993) showed that at least some of the additional ﬂow ends up in the bubble phase. However, it is not clear how long the additional moles generated stay in the dense phase or whether they transfer very quickly to the bubble phase. In our simulations, shown in Figure 6.4, two cases are compared at different oxygen concentrations, in order to evaluate the magnitude of uncertenity of the different assumptions. In “case a” a secondary gas is transferred only into the bubble phase. Through mass transfer between both phases the oxygen is

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Figure 6.4 Inﬂuence of the distribution of the secondary gas between bubble and suspension phase. Case “a”: secondary gas is transferred only into the bubble phase.

Case “b”: secondary gas is distributed into both phases. c(C2H6) = 1 vol%, u = 0.45 m/s, mCat/F = 700 kg·s/m3,Fs/Fp = 1.0, T = 590 °C.

transported into the suspension phase. “Case b” assumes that the secondary gas is injected into both phases according to their fractions. Both scenarios assume that the gas velocity through the suspension phase is constant. The excess gas is transferred by convection into the bubbles. The simulated ethane conversion and ethylene selectivity in Figure 6.4 demonstrate a large difference (up to 15%) between the two scenarios. In case “a”, where the oxygen level in the suspension phase is signiﬁcantly inﬂuenced by mass transfer limitations between the bubble and suspension phases, ethane conversion increases more slowly with increasing oxygen amount in the feed than in “case b” with direct oxygen distribution to bubbles and suspension. The higher oxygen to ethane ratio in case “b” explains the signiﬁcant enhancement of ethane conversion and loss of ethylene because of total oxidation to carbon oxides. These tendencies disagree with our experimental observations (see Section 6.3.4), in which the ethane conversion rises slow with increasing oxygen partial pressure. Therefore we assumed in the next simulation that the secondary gas is fed into the bubbles and subsequently the oxygen is transfered to the suspension phase. The empirical correlations used were neither ﬁtted to the experimetal data nor modiﬁed. Nevertheless, this dosing concept needs further investigation regarding the ﬂuidized-bed hydrodynamics. 6.2.3 Comparison Between Co-Feed and Distributed Oxygen Dosage

In the following simulation study the reactor concepts of co-feed and distributed oxygen dosage are compared with regard to achievable ethane conversions, ethylene selectivity and ethylene yield. The goal of this study was to identify attractive operating ranges for the application of FBMRs and the estimation of reactor performance in comparison to a conventional FLBR. The calculations were carried out with both reactor models at a constant temperature of 590 °C, as in Chapter 5. In order to cover a wide operation range, the oxygen concentration was varied

6.2 Modeling of the Distributed Reactant Dosage in Fluidized Beds

between 0.5 and 5.0 vol% and the contact time was adjusted between 700 and 1875 kg s/m3. The ethane concentration was kept constant at 1 vol% in all calculations. Figure 6.5 shows the simulated ethane conversion, ethylene selectivity and yield for both reactor concepts. Below 2 vol% O2 the conversion strongly depends on the concentration. In this range, the model predicts a slow rise of ethane conversion in the FLBMR. This can be explained with the lower local oxygen concentration. The ethane and the oxygen proﬁles of both dosing concepts are depicted in Figure 6.6. The chemical reaction in the suspension and the mass transfer limitations between the phases deﬁne the lower mole fractions in the suspension. In the FLBMR the low oxygen level results from feed distribution via the membranes; however a large amount of oxygen is captured in the bubbles and does not reach the reaction zone. This hinders the ethane conversion and enhances the ethylene selectivity due to the low oxygen to ethane ratio.

Figure 6.5 Simulation study for comparison of FLBR and FLBMR (gray: FLBR; black: FLBMR). c(C2H6) = 1 vol%, c(O2) = 0.5–5.0 vol%, T = 590 °C, mCat/F = 700–1875 kg·s/m3, Fs/Fp = 1.0.

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6 Fluidized-Bed Membrane Reactors

Figure 6.6 Simulated proﬁles of oxygen and ethane in the FLBR (gray) and in the FLBMR (black). Solid line: suspension phase; dashed line: bubble phase. c(O2) = 2 vol%, c(C2H6) = 1 vol%, T = 590 °C, mCat/F = 1875 kg·s/m3, Fs/Fp = 1.0.

The reactor comparison was made at identical volumetric ﬂow rate, thus the local gas velocity in the FLBR is always higher than in the FLBMR. Because mass transfer limitations between bubble and suspension phase increase with higher ﬂuidisation velocity due to increasing bubble size and bubble rise velocity, the dependency of ethane conversion on contact time is slightly higher for the FLBR. As expected, the ethylene selectivity decreases with increasing oxygen concentration. The lower oxygen partial pressure in the FLBMR results in much higher ethylene selectivity compared to co-feeding. Considering the ethylene yield, the FLBMR is less sensitive regarding the oxygen concentration, which results in a broader yield maximum. The simulation results demonstrate a better performance of the distributed reactant feeding in a wide parameter range, compared to the conventional co-feed reactor. However, at very low oxygen concentrations a higher ethylene yield should be expected in the FLBR.

6.3 Experimental 6.3.1 Experimental Set-Up

The experiments for both reactor conﬁgurations, FLBMR and FLBR, were performed in the same pilot plant, depicted in Figures 6.7 and 6.8. It consists of a gas-dosing unit providing the ﬂuidization gas (1) and the permeation gas through the membranes (2), the pilot-scale reactor (3) with the catalyst and the membrane (4), a cyclone (5) and a washer (6) at the reactor outlet to collect particles from catalyst attrition and to avoid a carryover of ﬁnes into the

6.3 Experimental

(a)

(b)

179

(c)

Figure 6.7 Photo of the experimental set-up: a) ﬂuidized-bed reactor, b) bundle of four tubular sinter metal membranes, c) single tubular sinter metal membrane.

N2 1 – fluidization gas supply 2 – permeation gas supply 3 – reactor 4 – fluidized catalyst bed with membrane 5 – cyclone 6 – washer 7 – gas chromatograph

air C2H6 air N2 N2 Figure 6.8

Schematic of the FLBMR and FLBR plant.

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6 Fluidized-Bed Membrane Reactors

environment (see Figure 6.8). Reactant and product gas streams are analyzed by gas chromatography (7) The gas-dosing unit is equipped with electronic mass ﬂow controllers allowing preparation of the desired compositions of reactant gases in the different experiments. Nitrogen and ethane had a purity of 99.998 and 99.95%, respectively. Air (dried) was provided by a compressor. The mixed ﬂuidization gas could be heated by a separate electrical pre-heater. In the case of FLBMR measurements C2H6/N2 mixtures were used for ﬂuidization and the oxidant (air or an air/ nitrogen mixture) was dosed in a distributed manner over the installed sintered metal membranes. During the FLBR experiments no membrane was installed inside the reactor and the complete reactant mixture was fed as ﬂuidization gas. The reactor was made of stainless steel (AlCr, Sicromal) and had an inner crosssection of 100 × 100 mm and a total height of 2.1 m. The preheated ﬂuidization gas entered the reaction zone through a sintered metal plate (Inconel) with an average pore diameter of 20 μm and 43% porosity. A spiral wound electrical heater was used to heat the reactor walls. Additionally, reactor walls were insulated with a ceramic ﬁber banket. The membranes (sintered porous tubular stainless steel membrane with dead-end conﬁguration, GKN Sinter Metals Filters), used as an inert oxidant distributor in the FLBMR, had a length of 165 mm, inner and outer diameters of 3 and 6 mm, respectively, and an average pore diameter of 8 μm. The metal membrane was selected because of its better thermal stability and mechanical strength, compared to ceramic membranes. The four membrane tubes were vertically mounted in the reaction zone directly above the gas distributor. The oxidant as permeation gas was fed from the top of the tube in the opposite direction to the ﬂuidization gas. Temperature was measured by NiCr/Ni thermocouples at three different vertical positions within the reactor: at the inlet, at the center of ﬂuidized catalyst bed and at the outlet of the reaction zone. Gas samples were taken at the reactor inlet and downstream of the cyclone, using a small membrane pump and were analyzed using a gas chromatograph. The gas chromatograph (HP6890, Agilent Technologies) operated with helium as carrier gas and was equipped with an TCD and an FID; two capillary columns (PoraPlot Q and PlotMolesieve) allowed the separation of ethane, ethylene, CO, CO2, O2 and N2. The carbon balance was accurate typically within ±3%. The γ-alumina supported vanadium oxide catalyst was applied as bed particles with a diameter of 0.44 mm and a particle density of 1316 kg/m3. Details about the preparation process are given by Klose et al. (2004b). 6.3.2 Experimental Procedure

The experiments in both operation modes were performed at atmospheric pressure. The reactor was preheated with air as a ﬂuidizing gas until the desired temperature was reached. Subsequently, the air was replaced by nitrogen and the appropriate reactant mixture. Measurement of the gas samples was carried out after 20–60 min, after a steady state was reached. Every measurement was repeated three times. The absence of wall and gas phase reactions was tested with the empty

6.3 Experimental

reactor up to 630 °C and with inert α-Al2O3 particles up to 600 °C; and less than 2% ethane conversion was found. The temperature distribution in the catalyst bed was measured in axial and radial directions under reaction conditions in the FLBR and in the FLBMR. The temperature differences in the reaction zone were below 2–3 K for both reactor types and showed isothermal conditions in the catalyst bed. 6.3.3 Results and Discussions

The performance of both dosing strategies – co-feed and segregated reactant distribution – was studied by varying the oxygen concentration, the temperature and the contact time (superﬁcial gas velocity). The ratio of the secondary gas to primary gas was a additional operation parameter in the FLBMR, which inﬂuenced the local concentration as well as the residence time proﬁles and was studied by feeding different gas amounts through the membranes. Separate experiments were carried out applying a mixed dosing strategy with simultaneous supply of oxygen at the reactor inlet and through the membranes. 6.3.4 Inﬂuence of the Oxygen Concentration

To show the inﬂuence of the local distribution of the reactants the oxygen concentration was varied for both conﬁgurations (FLBR, FLBMR) in the range of 0.6– 3.7 vol%, while the ethane concentration was kept constant (1 vol%). The experiments were performed at a temperature of 590 °C and a contact time of 1750 kg s/m3. To increase the oxygen concentration in the FLBR, nitrogen was stepwise replaced by air at a constant total gas volume ﬂow. In the FLBMR only the composition of the secondary gas was varied, to keep a constant secondary to primary gas ﬂow ratio. Both ethane conversion and the selectivity and yield of ethylene are compared in Figure 6.9. For the FLBR one can distinguish between two oxygen concentration ranges: The ﬁrst one with low oxygen concentration (0.6–1.5 vol%) is characterized by a distinct ethane conversion dependency. A small increase in the O2 concentration leads to a signiﬁcant conversion enhancement. Close to the stoichiometric ratio of the oxidative dehydrogenation of ethane (ODHE), the reaction rate depends strongly on the oxygen concentration. Above 1.5 vol% the inﬂuence of oxygen concentration on conversion decreases. Compared to the FLBR, the FLBMR shows no conversion plateau. Over the wide range of studied oxygen concentrations, conversion in the FLBR is higher than that in the FLBMR. To reach higher conversions by distributed dosing, a larger oxygen concentration or a higher O2/C2H6 ratio compared to the FLBR is needed. In contrast, ethylene selectivity is signiﬁcantly higher in the FLBMR and the loss of ethylene selectivity with increasing oxygen supply (due to higher COx formation rates) in the FLBMR is less pronounced than that in the FLBR. Under oxygen-limiting conditions, the main product is ethylene. Above 1.5 vol% the ethylene selectivity in the FLBR is nearly constant. The better

181

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6 Fluidized-Bed Membrane Reactors

Experiment: FLBMR FLBR

Simulation: FLBMR FLBR

Figure 6.9 Variation of the oxygen concentration. c(C2H6) = 1 vol%, T = 590 °C, mCat/F = 1750 kg·s/m3, Fs/Fp = 1.0.

performance of the FLBMR concept is more obvious from the selectivity–conversion diagram. Applying a distributed dosing startegy, 7–8% higher ethylene selectivity was reached at an identical ethane conversion. Considering the ethylene yield a maximum can be observed in both reactor conﬁgurations. For the FLBR this maximum appears at 1 vol% O2, while for the FLBMR the yield maximum is broader between 1.5 and 2.5 vol% O2 and is less sensitive regarding the oxygen concentration. The higher oxygen amount is needed to compensate for the shorter residence time of the oxygen molecules in the reaction zone. Under oxygen excess conditions the ethylene yield is up to 9% higher in the FLBMR compared to the FLBR. This behavior can be clearly attributed to the decreased average axial oxygen concentration in the FLBMR caused by the distributed oxidant and was also partially observed for packed-bed membrane reactors (Klose et al., 2004a). These results show a very good agreement between the simulations and the experiments for the FLBR and reproduce the main tendencies for the FLBMR. As described in Section 6.2.1, the discrepancies are the consequence of the model simpliﬁcations and the coarse empirical correlation for the ﬂuid dynamic parameters of the ﬂuidized bed.

6.3 Experimental

Measurement: FLBMR FLBR

Simulation: FLBMR FLBR

Figure 6.10 Variation of the temperature under oxygen excess conditions. c(C2H6) = 1 vol%, c(O2) = 3.7 vol%, mCat/F = 1750 kg·s/m3, Fs/Fp = 1.1.

6.3.5 Inﬂuence of the Temperature

Both reactor concepts were compared under oxygen excess conditions in the temperature range between 540 °C and 590 °C. The ethane concentration was 1 vol% and the oxygen concentration was set to 3.7 vol%. The course of the curves in Figure 6.10 show, in contrast to oxygen limiting conditions, a distinct dependency of the reactor performance on the bed temperature. Comparing the two reactors, ethane conversion is slightly higher in the FLBMR compared to the FLBR (especially at T = 540 °C). Co-feeding (FLBR) shows an increase in ethane conversion from 49 to 72 vol%, while the FLBMR delivers a stronger conversion increase from 55 to 74 vol%. The lower ethane conversion may have different reasons. One reason can be the lower average residence time of the ethane molecules in the FLBR (Tonkovich et al., 1996; Pena et al., 1998, Klose et al., 2004b), but this probably plays no role due to the long contact times. More reasonable is that the higher back-mixing affects and the larger bypass

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6 Fluidized-Bed Membrane Reactors

fraction in the FLBR leads to a lower conversion in comparison to the FLBMR, because the higher primary gas ﬂow promotes the formation of larger bubbles. This results in a larger bypass and a reduced mass transfer rate between the suspension and bubble phases in the FLBR. The difference in ethane conversion between the two reactor concepts becomes smaller with increasing temperature. Higher temperature leads to lower ethylene selectivities in both reactors due to increased carbon oxide formation. However, by distributing the oxygen along the reactor height, total oxidation can be suppressed more efﬁcinetly in the FLBMR for identical overall oxygen amounts in the feed. Furthermore, the lower backmixing in the FLBMR enhances ethylene selectivity. Comparing the concepts at same ethane conversion the ethylene selectivity was 9% higher in the FLBMR over the whole range studied. Remarkable again is the superiority of the membrane reactor regarding ethylene yield. The maximum ethylene yield is 8% higher in the FLBMR (27.8%) in comparison to the FLBR (18.9%). 6.3.6 Inﬂuence of the Superﬁcial Gas Velocity

The performance of the ﬂuidized bed depends on the ﬂuid dynamics, which are inﬂuenced by the particle properties, bed heights, ﬂuidization medium and ﬂuidization velocity. In order to investigate the inﬂuence of the ﬂuid dynamics on reactor performance, varying the ﬂuidization gas velocity for both dosing strategies were carried out between 4umf and 10umf (umf,500°C = 0.05 m/s). The gas velocities are related to the total gas volume ﬂow. To rule out the inﬂuence of other parameters, the primary to secondary gas ﬂow ratio was kept constant. The results of this study are depicted in Figure 6.11. The tendencies correspond to the results from the literature reported on bubbling ﬂuidized beds (Levenspiel, 1999; Kunii and Levenspiel, 1992). An increase in the gas velocity leads to a decrease in the conversion in both reactors. The FLBR shows higher ethane conversion but has a more pronounced sensitivity regarding the ﬂuidization velocity. Increasing the primary gas ﬂow by a factor of two, ethane conversion decreases by 14% in the FLBR. The conversion loss is only 6% in the FLBMR, which is attributed to the 50% lower primary gas ﬂow and, thus, to the smaller bubble fraction compared to the co-feed FLBR. The latter was also reported by Deshmukh et al. (2005a, 2005b). The bubble phase fraction and the bubble size increases with increasing gas velocity and hence reduces the contact time of the reactants as well as the mass transfer rate between the bubble and suspension phases. At higher gas velocities a larger fraction of ethane ﬂows into the bubbles and has therefore no contact with the catalyst surface. Due to the lower oxygen concentration in the feed the effect of the contact time on the ethylene selectivity is negligible. Altough the ethane conversion is lower, the higher selectivity in the FLBMR leads to 4% higher ethylene yield. The more relevant comparison made at identical ethane conversion demonstrates once again the main advantage of the membrane-dosing concept.

6.3 Experimental Experiment: FLBMR FLBR

Simulation: FLBMR FLBR

Figure 6.11 Variation of the superﬁcial gas velocity: c(C2H6) = 1 vol%, c(O2) = 1 vol%, T = 590 °C, Fs/Fp = 1.1.

A good agreement between model and experiments could be achieved for the conversion in the FLBR. The differences for the FLBMR could be the result of the correlations used by the calculation of the bubble fractions, which were obtained for ﬂuidized beds without secondary gas injection. 6.3.7 Inﬂuence of the Secondary to Primary Gas Flow Ratio

The experimental results above show that remarkable improvements in the ethylene selectivity can be achieved in both reactor concepts by decreasing the oxygen amount in the feed. However, in most cases this results in a decreased ethane conversion. Furthermore, as reported by many researchers, the distributed oxygen dosing may lead to a high hydrocarbon to oxygen ratio close to the reactor inlet, which can result in catalyst deactivation, coking and further undesirable side reactions. The dosage of small amounts of oxygen in the primary gas ﬂow or an increase in the secondary to primary gas ﬂow ratio can counteract these effects. In this section the latter is investigated.

185

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6 Fluidized-Bed Membrane Reactors

Figure 6.12 Variation of the secondary to primary gas ﬂow ratio: c(C2H6) = 1 vol%, T = 590 °C, mCat/F = 1000 kg s/m3.

The theoretical study shows that higher secondary gas fraction leads to an increase in the local oxygen concentration at the reactor inlet, which generates a higher average oxygen concentration throughout the bed. A ﬂuidized bed is also characterized by back-mixing effects, which inﬂuences these proﬁles and which also depends on gas velocity, bed height, catalyst particles, etc. The results in Figure 6.12 show the tendencies as function of the secondary gas fraction at different O2 concentrations in a range from 0.5 to 4.0 vol%. For comparison, the corresponding FLBR results are shown at Fs/Fp = 0 (cofeed). The conversion shows the typical increase for all feed ratios with increasing feed concentration. Depending on the oxygen concentration, one can distinguish between two ranges. Under oxygen excess conditions (2 and 4 vol%) the ethane conversion rises with increasing secondary gas fraction. The FLBR shows lower conversions (53%) than the FLBMR (56 and 67%, for 2 and 4 vol%, respectively) at a ﬂow ratio of 2/1. By contrast, in the range of stoichiometric feed concentrations the conversion is higher in the case of co-feeding. The decrease in conversion in the FLBMR is signiﬁcant, and it can be reduced by increasing the secondary

6.3 Experimental

gas ﬂow, but it remains below the values of the FLBR even at high (2/1) ﬂow ratios. This diagram shows once again the strong dependence of conversion on the local reactant concentration (see Section 6.3.4). A strong selectivity increase can be reached by distributed oxygen dosing at stoichiometric feed concentrations (70% selectivity at 0.5 vol% O2)., However, unlike the ethane conversion, the ethylene selectivity is hardly affected by the ﬂow ratio. At 4 vol% oxygen concentration, where the change in the selectivity is most pronounced, increasing the ﬂow ratio results in small decrease of only 2%. A high secondary to primary gas ﬂow ratio seems to be beneﬁcial for the ODHE reaction. At the same total gas feed, 6–9% higher ethylene yields can be reached by utilizing the ﬂow ratio as an additional degree of freedom in the FLBMR in comparison to the conventional reactor. 6.3.8 Inﬂuence of Distributed Reactant Dosing with Oxygen in the Primary Gas Flow

The previous parameter studies have shown a signiﬁcant improvement of the ehtylene selectivity and ethylene yield in the FLBMR in comparison with the FLBR. Nevertheless, ethane conversions in the FLBMR were lower in some cases even under oxygen excess conditions. It has been shown that increasing the secondary gas fraction leads to higher conversions under otherwise identical overall feed compositions. Alternatively, a combined dosing strategy can be applied by feeding part of the total oxygen amount at the reactor inlet. Besides the two studied dosing variants, which in fact can be regarded as extremes, FLBMR and FLBR, an additional conﬁguration was examined, which had an oxygen distribution between the primary and membrane feeds with a ratio of 1/1 (comb. FLBMR). For all dosing strategies the concentration of oxygen in the overall feed was the same. The secondary to primary gas ﬂow ratio was set to 1/1. The results are given in Figure 6.13. It can be seen that, in the absence of oxygen in the primary gas (FLBMR), the ethane conversion is lower, especially under oxygen excess conditions. The combined dosing strategy shows a signiﬁcant conversion increase even compared to the FLBR. In this case only enough oxygen is fed through the membranes to compensate the dilution of the primary gas. In the absence of chemical reactions a constant oxygen proﬁle over the bed height would result, similar to a FLBR. The ethane conversion is up to 8% higher, which is a result of the longer contact time and the lower back-mixing. As expected, the highest ethylene selectivity can be observed in the experiments in the FLBMR without primary oxygen feeding. By dosing oxygen at the inlet, the local oxygen concentration rises, which leads to a higher oxygen to hydrocarbon ratio and thus to a decreased ethylene selectivity. However, the measured selectivity is still up to 10% higher for the combined dosing than for the FLBR. From the selectivity versus conversion plot it seems that the combined dosing strategy has no signiﬁcant advantage, compared to a FLBMR. It should be however taken into consideration that a less reduced catalyst shows a lower afﬁnity for coking and hence can reach a longer operation time.

187

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Figure 6.13 Variation of the oxygen conditions in the primary gas ﬂow: c(C2H6) = 1 vol%, Tbed = 590 °C, mCat/F = 1400 kg s/m3, Fs/Fp = 1.0.

6.4 Conclusions

The performance of distributed reactant dosing in a FLBMR was studied in comparison to conventional co-feeding in a ﬂuidized bed. Both reactant dosing strategies were evaluated for the model reaction of oxidative dehydrogenation of ethane to ethylene under various experimental conditions. The beneﬁcial effect of oxidant dosing via membranes was most pronounced at high temperatures and moderate oxygen excess. Signiﬁcantly higher values for selectivity and yield of ethylene were achieved, however, at a moderate lower level of ethane conversion in comparison to co-feeding. To reach even higher conversions by distributed dosing, a larger oxygen concentration or a higher O2/C2H6 ratio than in the FLBR is needed. The higher amount of oxygen compensates the shorter residence time of the oxygen molecules in the reaction zone. Under oxygen excess conditions the ethylene yield is up to 9% higher in the FLBMR than in the FLBR. This could be due to the higher average contact time

Special Notation not Mentioned in Chapter 2

of the ethane and less mass transfer limitations because of reduced bubble size and bubble fraction (Deshmukh, 2004; Kleijn van Willigen et al., 2005; Christensen, Coppens, and Nijenhuis, 2005). The latter aspect also explains the fact that the co-feeding shows a more pronounced senstivity regarding the ﬂuidization velocity, where increasing the gas ﬂow leads to a stronger ethane conversion decrease in the FLBR than in the FLBMR. Furthermore it was demonstrated that an alternative to improve the conversion in the FLBMR is the increase of the secondary to primary gas ﬂow ratio or the dosage of small amounts of oxygen in the primary gas ﬂow. The combined dosing strategy does not lead to an improvement in the ethylene yield but can be useful to avoid the catalyst coking at low oxygen concentrations. A phenomenological two-phase dispersion model was applied to describe the effects of segregated reactant dosage on the reactor performance in ﬂuidized beds and to identify attractive parameter ranges for reactor operation. The results show a good agreement between the simulations and the experiments for the co-feeding and reproduce the main tendencies for distributed reactant feeding. The discrepancies are the consequence of the model simpliﬁcations and the coarse empirical correlation for the ﬂuid dynamic parameters of the conventional ﬂuidized bed.

Special Notation not Mentioned in Chapter 2 Latin Notation

a D F H j k ˙ m m M n Pe R S u u Um X Y z

m3/m2 m m3/s m kg/m2s m/s kg/s kg g/mol

J/mol K % m/s m m % % m

speciﬁc surface area diameter volumetric ﬂow rate height mass ﬂux mass transfer coefﬁcient mass ﬂow rate mass of solids molar mass number Péclet number universal gas constant selectivity superﬁcial velocity circumference perimeter conversion yield height coordinate

189

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6 Fluidized-Bed Membrane Reactors

Greek Notation

D εb εs ρ ω

m2/s

kg/m3

diffusion coefﬁcient bubble fraction void fraction in the emulsion density mass fraction

Subscripts and Superscripts

0 app b bed elu mf

at superﬁcial velocity conditions apparatus bubbles, bypass bed at elutriation point at minimum ﬂuidization

p Q rel s

primary convective ﬂow relative suspension gas, secondary

References Adris, A.M., Lim, C.J., and Grace, J.R. (1993) The effect and implications of gas volume increase due to reaction on bed expansion, bubbling and overall conversion in a ﬂuidized bed reactor. A.I.Ch.E. Annual Meeting, St. Louis, November 7–12, 1993. Adris, A.M., Lim, C.J., and Grace, J.R. (1997) The ﬂuidized-bed membrane reactor for steam methane reforming: model veriﬁcation and parametric study. Chem. Eng. Sci., 52 (10), 1609–1622. Ahchieva, D., Peglow, M., Heinrich, S., Mörl, L., Wolff, T., and Klose, F. (2005) Oxidative dehydrogenation of ethane in a ﬂuidized bed membrane reactor. Appl. Catal. A Gen., 296 (2), 176–185. Alonso, M., Lorences, M., Pina, M., and Patience, G. (2001) Butane partial oxidation in an externally ﬂuidized bed membrane reactor. Catal. Today, 67 (1–3), 151–157. Alonso, M., Lorences, M.J., Patience, G.S., Vega, A.B., Diez, F.V., and Dahl, S. (2005)

Membrane pilot reactor applied to selective oxidation reactions. Catal. Today, 104 (2–4), 177–184. Al-Sherehy, F., Grace, J.R., and Adris, A.E.M. (2004) Gas mixing and modeling of secondary gas distribution in a bench-scale ﬂuidized bed. AIChE J., 50 (5), 922–936. Al-Sherehy, F., Grace, J.R., and Adris, A.E.M. (2005) The inﬂuence of distributed reactant injection along the height of a ﬂuidized bed reactor. Chem. Eng. Sci., 60 (24), 7121–7130. Bokkers, G.A., Laverman, J.A., van Sint Annaland, M., and Kuipers, J.A.M. (2006) Modelling of large-scale dense gas-solid bubbling ﬂuidized beds using a novel discrete bubble model. Chem. Eng. Sci., 61 (17), 5590–5602. Chen, Z., Yan, Y., and Elnashaie, S.S.E.H. (2003) Novel circulating fast ﬂuidized-bed membrane reformer for efﬁcient production of hydrogen from steam reforming of methane. Chem. Eng. Sci., 58, 4335–4349.

References Christensen, D.O., Coppens, M.O., and Nijenhuis, J. (2005) Residence times in ﬂuidized beds with secondary gas injection. Proceedings of the AIChE Annual Meeting, Cincinnati, OH. Deshmukh, S. (2004) Membrane assisted ﬂuidized bed reactor. University of Twente, PhD thesis, The Netherlands. Deshmukh, S.A.R.K., Laverman, J.A., Cents, A.H.G., van Sint Annaland, M., and Kuipers, J.A.M. (2005a) Development of a membrane assisted ﬂuidized bed reactor. 1: gas phase back-mixing and bubble to emulsion mass transfer using tracer injection and ultrasound. Ind. Eng. Chem. Res., 44 (16), 5955–5965. Deshmukh, S.A.R.K., Laverman, J.A., van Sint Annaland, M., and Kuipers, J.A.M. (2005b) Development of a membrane-assisted ﬂuidized bed reactor. 2. Experimental demonstration and modeling for the partial oxidation of methanol. Ind. Eng. Chem. Res., 44 (16), 5966–5976. Deshmukh, S.A.R.K., Heinrich, S., Mörl, L., van Sint Annaland, M., and Kuipers, J.A.M. (2007) Membrane assisted ﬂuidized bed reactors: Potentials and hurdles. Chem. Eng. Sci., 62 (1–2), 416–436. Dixon, A. (2003) Recent research in catalytic membrane reactors. Int. J. Chem. Reactor Eng., Review R6, 1. Hilligardt, K. (1986) Zur Strömungsmechanik von Grobkornwirbelschichten. PhD thesis, TU Hamburg-Harburg. Hilligardt, K., and Werther, J. (1986) Local bubble gas hold-up expansion of gas/solid ﬂuidized beds. Ger. Chem. Eng., 9, 215–221. Jin, Y., Wei, F., and Wang, Y. (2003) Effect of internal tubes and bafﬂes, in Handbook of Fluidisation and Fluid-Particle Systems (ed. W.-C. Yang), Marcel Dekker, pp. 171–200. Kleijn van Willigen, F., Christensen, D., Ommen, J.R.V., and Coppens, M.O. (2005) Imposing dynamic structures on ﬂuidized beds. Catal. Today, 105 (3–4), 560–568. Klose, F., Wolff, T., Thomas, S., and Seidel-Morgenstern, A. (2004a) Appl. Catal. A Gen., 257, 193–199. Klose, F., Joshi, M., Hamel, C., and Seidel-Morgenstern, A. (2004b) Selective

oxidation of ethane over a VOx/-Al2O3 catalyst – investigation of the reaction network. Appl. Catal. A Gen., 260 (1), 101–110. Kunii, D., and Levenspiel, O. (1992) Fluidization Engineering, John Wiley & Sons, Inc., New York. Lee, G.S., and Kim, S.D. (1989) Gas mixing in slugging and turbulent ﬂuidized beds. Chem. Eng. Commun., 86, 91–111. Levenspiel, O. (1999) Chemical Reaction Engineering, John Wiley & Sons, Inc., New York. Marcano, J.G.S., and Tsotsis, T.T. (2002) Catalytic Membranes and Membrane Reactors, Wiley-VCH Verlag GmbH, Weinheim. Miracca, I., and Capone, G. (2001) The staging in ﬂuidized bed reactors: from CSTR to plug-ﬂow. Chem. Eng. J., 82, 259–266. Mleczko, L., Schweer, D., Durjanova, Z., Andorf, R., and Baerns, M. (1994) Reaction engineering approaches to the oxidative coupling of methane to C2 hydrocarbons. Stud. Surf. Sci. Catal., 8, 155–164. Patil, C.S., van Sint Annaland, M., and Kuipers, J.A.M. (2005) Design of a novel autothermal membrane-assisted ﬂuidized-bed reactor for the production of ultrapure hydrogen from methane. Ind. Eng. Chem. Res., 44 (25), 9502–9512. Pena, M., Carr, D., Yeung, K., and Varma, A. (1998) Ethylene epoxidation in a catalytic membrane reactor. Chem. Eng. Sci., 53 (22), 3821–3834. Poling, B., Prausnitz, J.M., and O’Connell, J.P. (2001) Properties of Gases and Liquids, 5th edn, McGraw-Hill Book Company, New York. Ramos, R., Pina, M., Menendez, M., Santamaria, J., and Patience, G. (2001) Oxidative dehydrogenation of propane to propene, 2: Simulation of a commercial inert membrane reactor immersed in a ﬂuidized bed. Can. J. Chem. Eng., 79 (6), 902–912. Saracco, G., Neomagus, H.W.J.P., Versteeg, G.F., and Swaaij, W.P.M. (1999) High-temperature membrane reactors. Potential and problems. Chem. Eng. Sci., 54 (13–14), 1997–2018. Tonkovich, A.L., Zilka, J., Jimenez, D., Roberts, G., and Cox, J. (1996) Experimental

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6 Fluidized-Bed Membrane Reactors investigations of inorganic membrane reactors: a distributed feed approach for partial oxidation reactions. Chem. Eng. Sci., 53 (5), 789–806. Volk, W., Johnson, C.A., and Stotler, H.H. (1962) Effect of reactor internals on quality of ﬂuidization. Chem. Eng. Prog., 58 (3), 44–47. Werther, J., and Schössler, M. (1999) Modeling catalytic reactions in bubbling

ﬂuidized beds of ﬁne particles. Proceedings of the 6th International Conference on Circulating Fluidized Beds, 357–368, Würzburg, Germany. Westermann, T., and Melin, T. (2005) Membrane reactors. Chemie-IngenieurTechnik, 77 (11), 1655–1668.

193

7 Solid Electrolyte Membrane Reactors Liisa Rihko-Struckmann, Barbara Munder, Ljubomir Chalakov, and Kai Sundmacher

7.1 Introduction

The present chapter introduces a speciﬁc type of membrane reactor only brieﬂy mentioned in Chapter 1. The solid electrolyte membrane reactors (SEMR) – or electrochemical membrane reactors as they also are called – are equipped with ion-conducting membranes, which ideally are impermeable for non-charged reaction species. These reactors operate as electrochemical cells, in which the oxidation and reduction reactions are carried out separately on catalyst/electrodes layers located on the opposite sides of the electrolyte. The development of solid electrolyte membrane reactors has reached a semi-commercial stage in fuel cells, in which the maximal generation of electric energy by the total oxidation of hydrogen or hydrocarbon feeds is the primary goal of operation. Research on chemical reactor applications is strongly concentrated in the high-temperature range using either oxygen ion- or proton-conducting inorganic membranes. Some interesting examples were published recently, investigating proton-conducting polymeric membranes for the production of chemicals. This chapter gives a brief overview on the current status and future trends in the development and application of solid electrolyte reactors equipped with solid electrolyte (SE) materials used as membranes in these reactors. Initially the working principle of a solid electrolyte membrane reactor and material aspects are discussed. The second part of the chapter gives a detailed description of the special aspects concerning the modeling of solid electrolyte membrane reactors, as well as the application examples of maleic anhydride (MA) synthesis and oxidative dehydrogenation of ethane. Finally the chapter reviews recent papers concerning solid electrolyte membrane reactors applying:

• • •

high-temperature oxygen ion conductors, high-temperature proton conductors, low-temperature proton conductors.

There are some recent review papers, especially written for high-temperature applications, which we would like to recommend to readers interested in more Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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7 Solid Electrolyte Membrane Reactors

detailed information on these materials (Marnellos and Stoukides, 2004). In 2000, Stoukides gave an outlook on the applications of high-temperature oxygen SE membrane reactors (Stoukides, 2000). Iwahara et al. (2004) and Kokkoﬁtis et al. (2007) published reviews of hydrogen technology using proton-conducting ceramics. Bredesen, Jordal, and Bolland (2004) presented a survey of hightemperature membranes and applications of membrane reactors for integration in power generation cycles with CO2 capture, which is an important aspect in the power plant engineering. The cited reviews elucidate SE membranes from the chemical engineers’ point of view. The excellent reviews by Goodenough (2003) and Kreuer (2003) are recommended to readers who would like to be informed about material aspects of oxide ion-conducting or proton-conducting electrolytes, respectively.

7.2 Operational and Material Aspects in Solid Electrolyte Membrane Reactors 7.2.1 Classiﬁcation of Membranes

Aside from the porous membranes, for which the characteristics and aspects of modeling are described in detail in previous chapters in this book, two categories of gas-dense membranes can be classiﬁed, namely mixed ion/electron conductors (MIEC) and ion conductors (Sundmacher, Rihko-Struckmann, and Galvita, 2005). MIEC are those in which the values of ionic and electronic conductivity are comparable, whereas the latter is referred to solid electrolytes (SE) in which the ionic transfer numbers, that is, the fraction of electrical current transferred by the ions, is two or more orders of magnitude higher than that for electrons. The transport mechanisms of the electron (MIEC) and ion conductors are illustrated in Figure 7.1 using oxygen transport as example. MIEC have both high ionic and high electronic conductivities, whereas SE exhibit only high ionic but very low electronic conductivities. MIEC membrane reactors are simpler in design and construction than the SE reactors because both ions and electrons are transported internally, that is, inside the membrane material. SE membrane reactors require the external circuit for electron recycle to the cathode, but they provide therefore some speciﬁc beneﬁts, as discussed later in detail. The transfer of oxygen occurs in the dense oxygen ion-conducting membranes in the form the ionic species, O2−, moving from vacancy to vacancy in the lattice of the solid material, driven by the electrostatic potential difference. The vacancies are created in a solid solution of oxides of di- and trivalent cations with oxides of tetravalent metals. Due to this transport mechanism, the permeability of oxygen is usually remarkably lower than in porous materials, which often limits the technical applicability of oxygen ion conducting solid electrolyte membrane reactors. But, as outlined later in this chapter, the permeability is strongly dependent on the operating temperature, whereas a high operating temperature enhances the

7.2 Operational and Material Aspects in Solid Electrolyte Membrane Reactors

Dense Membranes

Porous Membranes • oxygen transfer as O2 molecules • high permeability • moderate permselectivity • depends on pore size / structure

• oxygen transfer as ionic species O2• good permselectivity of oxygen ⇒ integrated air separation • reactor efficiency limited by permeability (high T)

Mixed Ion Electron Conductors (MIEC) • σion high, σel high • internal circuit for electrons • simple reactor design

• alumina • silica • zeolites

μ1(O2)

O2(g)

195

μ1(O2)

μ2(O2)

• σion high, σel low • external circuit for electrons • complex reactor design

cathode

2 O2-

4 e-

Oxygen Ion Conductors / Solid Electrolytes (SE)

μ1(O2) μ2(O2)

4 e-

2 O2- anode

O2-

Figure 7.1 Classiﬁcation of ceramic membranes for oxygen transport. Reproduced from (Sundmacher, Rihko-Struckmann, and Galvita, 2005), reprinted with permission from Elsevier.

permeability of the SE material. Simultaneously, the permselectivities of SE membranes are excellent. When using air, that is, a mixture of oxygen and nitrogen, oxygen is transferred exclusively from one side to the other. Consequently, SE membranes allow a direct integration of air separation in the process, and any additional air separation is unnecessary. This in turn reduces the operating and investment costs of the oxidation process. Due to the electrochemical ion/electron transfer reactions in SE membranes, the electrode layers (anode, cathode) have to be constructed directly adjacent to the ion-conducting membrane. The design of SE reactors – especially the construction and fabrication of membrane–electrode interfaces – is complicated. But, the ionic conduction of the SE materials provides a unique tool for the control of SE membrane reactors. Due to the faradaic coupling of oxygen ﬂux and cell current, the galvanostatic control of the external ﬂux of electrons or, alternatively, the potentiostatic control of electrode potentials offers the opportunity to drive the reactions at the two electrodes in the desired direction. 7.2.2 Ion Conductivity of Selected Materials

Figure 7.2 shows a map of selected SE materials and their ionic conductivities as a function of temperature. In the group of proton conductors there are two main classes: (a) polymeric materials which can only be operated in the low-temperature

μ2(O2)

196

7 Solid Electrolyte Membrane Reactors Temperature T, [[°C]

50… 100….200 Nafion TM [1] σ25= 0.083 S/cm

300

400

500

600

700

800

900

BaZr(M)O 3 [5] σ800= 0.025 S/cm

Proton Conductors (H +)

PEEK [2] σ140= 0.04 S/cm

BaCe(Y)O 3 [4] σ800= 0.06 S/cm

PBI/PA [3] σ160= 0.065 S/cm

SrCe (Yb)O 3 [4] σ800= 0.0065 S/cm BaCe(Nb) O 3 [4] σ800= 0.02 S/cm

2-

) ( Oxygen Ion Conductors (O LaSrGaMgO [6] (LSGM) σ673= 0.034 S/cm

YSZ [6] σ818= 0.063 S/cm ScSZ [6] σ818= 0.103 S/cm

Figure 7.2 Ion conductivities of selected SE materials. Reproduced from (Sundmacher, Rihko-Struckmann, and Galvita, 2005), reprinted with permission from Elsevier. For references [1]–[6], see the original paper.

range up to 200 °C and (b) certain mixed oxides which show reasonable proton conductivities at about 500–900 °C. Typical representatives of low-temperature proton conductors are Naﬁon, polybenzimidazole (PBI) and polyetheretherketones (PEEK). Currently investigated high-temperature proton conductors are Ba–Zr, Sr–Ce and Ba–Ce mixed oxides. Oxygen ion conductors can be only operated in the high-temperature range. The most important materials here are yttriastabilized zirconia (YSZ), scandia-stabilized zirconia (ScSZ), and – nowadays extensively investigated – perovskite materials such as Sr/Mg-doped lanthan gallat (LSGM). It is interesting to note that the mentioned materials in the low and hightemperature range all have ion conductivities of similar magnitude, that is, around σ = 0.01–0.1 S cm−1. When applying SE materials in catalytic membrane reactors, it is important that the materials show suitable oxygen transport rates within the catalyst temperature operating window. As an example, for butane partial oxidation (POX) with the VPO catalyst, a SE membrane owing high oxygen permeability in the range between 400 and 600 °C would be optimal. Table 7.1 gives typical oxygen ﬂux densities for YSZ, ScSZ (with 9% Sc) and LSGM (Sundmacher, Rihko-Struckmann, and Galvita, 2005). As discussed in the previous section, the ﬂux densities of solid electrolytes are generally lower than those of typical porous membranes (supported microporous SiO2, mesoporous Al2O3), at the same temperature. 7.2.3 Membrane–Electrode–Interface Design in Solid Electrolyte Membrane Reactor

The schematic illustration in Figure 7.1 is a highly simpliﬁed representation of SE membrane reactors applying ion conductors. In reality SE membrane reactors have complicated multi-layered construction. The electrodes, where the electron/ ion transfer reactions occur, have to be ﬁxed on both sides of the ion-conducting

7.2 Operational and Material Aspects in Solid Electrolyte Membrane Reactors Total conductivity of solid electrolytes and calculated oxygen ﬂux for a membrane thickness of 250 μm (U = 1.0 V).

Table 7.1

Temperature

420 °C

624 °C

Material

Total conductivity

S m−1

YSZa) ScSZb) LSGMc)

0.018 0.011 0.092

0.80 1.34 2.32

Oxygen ﬂux density

mmol m−2s−1

0.188 0.114 0.949

8.3 13.9 24.1

YSZa) ScSZb) LSGMc)

a) yttria (13%). b) scandia (9%) stabilized zirconia. c) La0.9Sr0.1Ga0.85Mg0.15O3-δ.

membrane to be able close the charge circuit. They necessitate a close contact not only to the membrane but also to the electronic current collectors, which are directly connected to the external electron circuit. As a summary, in order to work optimally the electrode/catalyst layer has to fulﬁll the following requirements:

• • • •

a catalytic activity for the electrochemical and catalytic reactions, an electronic conductivity – electrons which are released in the anodic reaction or consumed in the cathodic reaction at the reaction sites, have to be collected, an ionic conductivity – the ions transferred through the membrane have to be conducted towards the reaction sites, porous structure inside of the electrode – the non-charged reactants have to be transported to the reaction sites.

Theoretically, the following four operations (electron conduction, ion conduction, catalytic activity, free access for gaseous feed) have to be possible in one location for the electrochemical reaction to occur. In order to combine the described operations, electrodes in SE membrane reactors are typically designed as gas diffusion electrodes (GDE), or more generally speaking, ﬂuid diffusion electrodes. Figure 7.3 shows a schematic illustration of a typical GDE. Optimal electrode design requires a perfectly executed balance of the different functions. This is often achieved by preparing mixtures of ion conducting particles (made of the membrane material), particles of electron conductor and particles with catalytic activity. In an optimal case, one metallic phase possesses both high electronic conductivity and high catalytic activity. Furthermore, by using well deﬁned particle size fractions of the materials or by carrying out thermal treatment, one can adjust

197

198

7 Solid Electrolyte Membrane Reactors Gas-filled pores

Catalyst Electron conductor Solid Electrolyte Membrane

Porous Current Collector

Ion conductor

Gas Diffusion Electrode Layer

Figure 7.3 Schematic illustration of gas diffusion electrode (GDE). Reproduced from (Sundmacher, Rihko-Struckmann, and Galvita, 2005), reprinted with permission from Elsevier.

the electrode pore structure. This in turn offers the possibility to optimize the transport properties of the GDE with respect to the non-charged reactants. 7.2.4 Operating Modi of Solid Electrolyte Membrane Reactors

Solid electrolyte membrane reactors can be operated in a variety of modi which are illustrated in Figure 7.4 using the hydrogen–oxygen reaction combined with an oxygen ion-conducting membrane as example. In the open circuit mode (icell = 0), the membrane reactor is operated potentiometrically as a sensor without any net current through the electrolyte. In this mode, the activity difference, which in most cases describes us the concentration difference of reactants, on both sides 0 of the solid electrolyte can be monitored via the open-circuit cell voltage E cell , often abbreviated as OCV, based on Nernst’s law. In the fuel cell mode, the cell current is positive (icell > 0) and the cell voltage is below the OCV level due to internal cell resistances. A precise control of the oxygen permeation rate is possible due to the faradaic coupling of oxygen ﬂux and the cell current. Cathodic reactants are reduced to ionic species at the cathodic electrode, and the ions are transferred through the membrane to the anodic electrode where they react with the anodic reactants. The DC power density, p = Ecell⋅icell, is positive, that is, one obtains electric power output from the electrochemical process (P > 0). In this mode, the negative ΔRG of the chemical reaction is converted directly into electrical energy, thereby reducing the amount of thermal energy being released during the reaction. The highly negative ΔRG of hydrocarbon oxidation reactions

7.2 Operational and Material Aspects in Solid Electrolyte Membrane Reactors

Direction of current

-

+

Cell Voltage, Ecell / [V]

0.5

1.0 0.5 0 -0.5

Sensor OCV: E0cell

0.3

0.1

E*

ilim

p*

-0.1

i* -0.3

Electrolyzer

-1.0 -250

Fuel cell

Ion Pump

-0.5

0

0.1

0

0.2

0.3

250

500

0.4

750

-2

i / [A m Current Density, icell ]/ [A m-2] cell

Figure 7.4 Operating modi of SE membrane 0 reactors. Electrolyzer: icell < 0, Ecell > Ecell , P < 0. 0 Sensor: icell = 0, Ecell = Ecell , P = 0. Fuel cell: 0 , P > 0. Ion pump: icell > 0, 0 < Ecell < Ecell

icell > 0, Ecell < 0, P < 0. Reproduced from (Sundmacher, Rihko-Struckmann, and Galvita, 2005), reprinted with permission from Elsevier.

enables high driving force and a positive cell voltage, positive power output and therefore allows the process to be operated in the self-driven fuel cell mode. In the case of partial oxidation reactions of, for example, hydrocarbons, the simultaneous generation of valuable chemicals and energy is possible in the fuel cell mode. If the current density is forced to exceed a certain limiting value ilim > 0, it is possible only as the cell voltage is negative. In this special form of electrolysis, in the ion pump mode, the direction of current is equal to the fuel cell mode, but the transfer of charged species through the solid electrolyte is supported with external electric energy input to the SE reactor (p < 0). Finally, the direction of the overall electrochemical reaction can be changed to the opposite one if negative cell currents are applied. In this classic electrolysis 0 mode, the cell voltage exceeds the OCV level ( E > E cell ) and the power is negative (p < 0). Then, the direction of the electronic current and the ionic ﬂux are opposite to the fuel cell mode. 7.2.5 Cell Voltage Analysis

The overall cell voltage Ecell of a solid electrolyte membrane reactor can be easily measured in experiments (Figure 7.5). However, the Ecell consists of several physical and electrochemical contributions and a detailed deconvolution of the cell voltage into:

199

200

7 Solid Electrolyte Membrane Reactors

Figure 7.5 Decomposition of cell voltage into main resistances. Reproduced from (Sundmacher, Rihko-Struckmann, and Galvita, 2005), reprinted with permission from Elsevier.

• • • •

0 open circuit cell voltage E cell (OCV), voltage drop due to the ohmic resistances (electrolyte membrane, the electrodes and the current collectors), concentration polarization due to mass transfer resistances within the electrode and due to the depletion of reactants from the reactor inlet up to the electrode, charge transfer resistances at the electrodes.

gives valuable information on how to improve the reactor performance. As listed in Figure 7.5, one system has various cell design parameters which should be changed in order to reduce the contribution of certain resistances. The most important factors are the thicknesses of the different cell layers, the intrinsic conductivities of the materials used, the amount of the catalyst applied and the construction of the electrode layer to quarantee a good contact between the ionic carrier, electron carrier as well as the catalyst. 7.2.6 Non-Faradaic Effects

An overview on SE membrane reactors cannot be written without – at least brieﬂy – mentioning the non-electrochemical modiﬁcation of catalyst activity effect (NEMCA). Normally the rates of electrochemical reactions taking place at the electrodes obey Faraday’s law, that is, the current ﬂowing through the membrane and the reaction rate at the considered electrode are proportional to each other. However, there are a couple of reactions where deviations from Faraday’s law were observed when the process is operated in a special mode – a mixed feed – in which one reac-

7.3 Modeling of Solid Electrolyte Membrane Reactors

tant, for example, oxygen, is simultaneously fed both gaseous as well as electrochemical pumping. If gaseous ethane and oxygen are fed and they react on a catalyst which is placed on top of an YSZ membrane which provides additional electrochemical oxygen supply, the catalytic rate increase during polarization can be higher than the calculated one from Faraday’s law. This is due to the electrochemical promotion of the catalytic reaction caused by the change of the electrostatic potential of the catalyst, as outlined in a series of papers by Vayenas and coworkers (see, e.g., Vayenas, Bebelis, and Ladas, 1990; Bebelis and Vayenas, 1989).

7.3 Modeling of Solid Electrolyte Membrane Reactors

The electrochemical reactions in solid electrolyte membrane reactors bring additional aspects to the system which have to be considered during modeling and which increase the complexity of the models of such reactors. Besides the heterogeneously catalyzed reactions and the possible mass transport resistances, the electrochemical charge transfer reactions on the elctrodes as well as the charge transfer in solid electrolytes have to be included in the model. In contrast to porous membranes where the driving force for the mass transfer through the membrane is related to the Δp over the membrane, in solid electrolyte membrane reactors the ion conduction through the membrane is driven by the electrical potential difference across the membrane. Membrane reactors are especially favorable for reaction kinetics in which the partial pressure of one component appears in a lower order in the desired reaction rate than in the rate expressions for the undesired reactions. In such a case a selectivity advantage can be achieved by a controlled distributed feed of the limiting component across an inert membrane. For example in the partial oxidation reactions, the local oxygen partial pressure could be lowered over the whole length of the reactor and the total oxidation reactions suppressed. In a solid electrolyte membrane reactor the faradaic coupling provides the unique tool for the precise dosing of the critical reagent (e.g., oxygen or hydrogen). Besides their concentration, the type and state of the oxygen species available at the active catalyst sites inﬂuence signiﬁcantly the reaction selectivity. This is especially cruicial in solid electrolyte reactors, where aside from gaseous O2 being released on the anode, other more active oxygen spieces might also exist and inﬂuence selectivity either positively or negatively. Eng and Stoukides (1991) and Wang and Lin (1995) reported that, in solid electrolyte membrane reactors, the oxygen anions (O2−) transported across the membrane might directly form selective oxygen species on the membrane or catalyst surface while gas-phase oxygen, which would rather give rise to unselective reactions, could be excluded from the reaction zone. Ye et al. (2006) and Chalakov et al. (2007) observed high reactivities for the desired intermediate, which was likely due to the additional electrochemical reactions between oxygen ions on the anode and the intermediate, as discussed later in detail.

201

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7 Solid Electrolyte Membrane Reactors

This chapter presents a general model for solid electrolyte membrane reactors which is capable of describing the prevailing physical phenomena taking place in such reactors (Munder et al., 2005). The partial oxidation of n-butane to maleic anhydride and the oxidative dehydrogenation of ethane are selected as model reactions and the kinetic models for both reactions are integrated into the developed reactor model. The partial oxidation of n-butane to maleic anhydride, on the one hand, is still the only industrial application of the direct partial oxidation of alkanes (Centi, Cavani, and Triﬁro, 2001) and, on the other hand, it exhibits the typical properties of selective oxidations. In our laboratory we (Ye et al., 2004) studied experimentally the feasibility of electrocatalytic synthesis for this reaction. However, theoretical analysis and model simulations are necessary in order to evaluate the reactor performance and to provide an efﬁcient design and optimal operation conditions. 7.3.1 Reactor Model for Systems Containing Solid Electrolyte Membranes

The following physical phenomena have to be considered in the modeling of an oxygen ion-conducting electrolyte membrane reactor for a heterogeneously catalyzed oxidation reaction. The charge in the form of oxygen anions, O2−, is transported by migration through the solid electrolyte membrane (SE, see Figure 7.6). Due to geometrical reasons – the membrane thickness is typically some orders of magnitude smaller than the surface dimensions – it can usually be assumed that the current ﬂows predominantly in the radial direction. On the surface between the electrolyte and the anodic catalyst layer (AC), both the electrochemical charge transfer reactions and the heterogeneously catalyzed

Figure 7.6 Schematic diagram of the SEMR. Reproduced from (Munder et al., 2005), reprinted with permission from Elsevier.

7.3 Modeling of Solid Electrolyte Membrane Reactors

gas phase reactions might take place. The reactions are coupled with diffusive mass transport through the catalyst pores for gaseous O2 and with charge transport in form of oxygen anions, O2−, and electrons, e−, through the solid phase of the catalyst layer, respectively. Both gas phase diffusion and oxygen ion transport occur predominantly in radial direction, whereas released electrons move in an axial direction toward the external electric circle. Finally, in the anodic gas compartment mass transport can be convective and diffusive. Assuming plug ﬂow along the anodic gas compartment without axial dispersion and neglecting possible radial concentration proﬁles in a ﬁrst approach, the complete system could be modeled one-dimensionally with respect to the anodic gas compartment (A) and one-plus-one dimensionally with respect to the solid electrolyte membrane (SE) and the porous anodic catalyst layer (AC). However, at this stage, in order to facilitate further model simpliﬁcations, it is reasonable to estimate the inﬂuence of the internal mass transfer resistances within the anodic catalyst layer (AC) in terms of dimensionless numbers. The Damköhler number of the second order, DaII, which is also known as the square of the Thiele modulus, gives an estimate of the ratio of the reaction rates to the diffusion rate under characteristic conditions and is deﬁned as: DaII = Φ2 =

2 (d AC ) ⋅ rref (T ) ⋅ MCat

D eff ⋅ ct ⋅ V

(7.1)

where rref stands for a (intrinsic) reference reaction rate. In the operating conditions typically applied for maleic anhydride synthesis (T = 350–550°C), using the kinetic parameters as given in the literature (Hess, 2002) [0.1–10.0 mol kgcat−1 s−1], and a catalyst layer thickness in the range 0.1–1.0 mm, the value for DaII is less than 10−2. This means, that due to the slow catalytic reactions, the gas diffusion resistance inside the catalyst pores could be neglected and the process is likely kinetically controlled. A second Damköhler number for electrochemical systems, DaIIel , can be written as the ratio of a characteristic electrochemical reaction rate to a characteristic O2− migration rate through the solid phase of the anodic catalytic layer (Munder et al., 2005). It can be calculated according to Equation 7.2: DaIIel =

d AC ⋅ rel,ref ⋅ F σ Oeff2− ⋅ ΔΦ max

(7.2)

Even if the ion-conductivity were estimated to be as high as 0.01 S m−1, the values for DaIIel higher than 10 would be reached due to the low operation temperature. Therefore, it is reasonable to assume here that, in the electrochemically supported MA synthesis, the charge transfer reactions take place within a very narrow region close to the membrane surface. From the above considerations, one can then conclude that, under the given operation conditions (Ye et al., 2004), the electrochemical MA synthesis can be practically divided into two locally separated reaction steps. The ﬁrst step comprises all charge transport processes and the electrochemical charge transfer reactions within the SE membrane and a narrow surface region of the electrodes. The second

203

204

7 Solid Electrolyte Membrane Reactors

covers all gas phase transport processes and heterogeneously catalyzed gas phase reactions. Due to the low diffusion resistances, the anode gas compartment (A) and the anodic catalyst layer (AC) are assumed to be one phase without concentration gradients in the radial direction and this can be modeled by a one-dimensional (axial direction) pseudo-homogeneous approach. The processes in this combined phase are coupled with the electrochemical processes via the radial oxygen ﬂow. Further assumptions can be made as follows. Due to the low reactant concentrations, the slow rate of reaction and the temperature control in the experimental setup, the reactor might be assumed to work under isothermal conditions. Furthermore, the pressure drop along the gas compartment is neglected, and the gas phase obeys the ideal gas law. The cathodic side is assumed to be a quasisteady-state oxygen reservoir without concentration change, which can be experimentally established by a sufﬁciently high air ﬂow rate through the cathode channel (C). Interfacial mass transfer resistances between the gas phases and solid surfaces of the membrane layers are assumed to be smaller than the diffusion resistances in the catalytic layers and are therefore neglected as well. Adsorption and desorption processes might have an inﬂuence but are not taken into consideration here. On the basis of the above assumptions, the following model (Equations 7.3 and 7.4) are obtained in addition of the general model equations in Chapter 2. The component balances for the gas phase species i on the anode side yield: ct

∂yi 1 ∂ (F A yi ) As M + =− ji + cat ∑ ν ijr j ∂t A z ∂z V V j

(7.3)

The assumed isobaric conditions and the ideal gas law lead to a quasi-stationary total mass balance for the anodic gas phase: 0=−

1 ∂F A A s + A z ∂z V

∑j i

i

+

M cat ∑ ∑ νijr j V i j

(7.4)

The ﬂow density ji(z) obeys Faradays law for oxygen, and is zero for all other gas phase components. The electrochemical processes can be represented by an equivalent circuit, as illustrated in Figure 7.7. The charge balance equations being speciﬁc for solid electrolyte membrane reactors, which were not discussed in Chapter 2, are presented in the following. Charge balances describe the anodic and the cathodic potential difference across the interfaces between the electrolyte and the respective electrode. ∂ΔΦ A ∂η A 1 = = ( icell − 2FrelA ) CDL ∂t ∂t ∂ΔΦ C ∂ηC 1 = = ( −icell − 2FrelC ) CDL ∂t ∂t

(7.5, 7.6)

Ohm’s law describes the potential drop across the solid electrolyte as well as along the electrodes.

7.3 Modeling of Solid Electrolyte Membrane Reactors

Cathode

Anode

R

R

Figure 7.7 Equivalent circuit representing the electrochemical model of the SEMR. Reproduced from (Munder et al., 2005), reprinted with permission from Elsevier.

ΔΦSE =

d SE icell σ SE (T )

A ∂ΔΦ CA = (R A + R C ) 2s L ∂z

(7.7) z =L

∫i

cell

dz

(7.8)

z = z

The local potential difference between cathode and anode at each point along the z-coordinate is calculated according to Kirchhoff’s law (Figure 7.9) ΔΦ CA = ΔΦ C − ΔΦSE − ΔΦ A C SE = ΔΦ CA − ηA 00 + η − ΔΦ

(7.9)

The cathodic and anodic overpotentials, η and η , include both the activation and concentration effects. Last, the integral of current densities over the reactor length is equal to the total cell current: A

I cell =

As L

C

z =L

∫i

cell

dz

(7.10)

z =0

and a modiﬁed Arrhenius type equation can be applied for the temperature dependence of the SE membrane conductivity: ⎛ E ⎞ σ SE (T ) ⋅ T = C SE ⋅ exp ⎜ − A ⎟ ⎝ RT ⎠ SE

(7.11)

205

206

7 Solid Electrolyte Membrane Reactors

7.3.2 Kinetic Equations for Charge Transfer Reactions

The reaction equations for the oxygen charge transfer reactions on the cathode and anode (Equations 7.12 and 7.13), are as follows: ⎯⎯ ⎯ → O2 − Cathode: 0.5 O2 + 2 e− ← ⎯

(7.12)

⎯⎯ ⎯ → 0.5 O2 + 2 e− Anode: O2 − ← ⎯

(7.13)

The rates of the electrochemical charge transfer reactions can be described by the Butler–Volmer equation (7.14): AC AC nF ⎛ E ⎞⎡ ⎛α relA C = k0A C exp ⎜ − A ⎟ ⎢exp ⎜ ⎝ ⎝ RT ⎠ ⎣ RT

AC ⎞ ⎛ (1 − α )nF A C ⎞ ⎤ η A C ⎟ − ( yO2 )0.5 exp ⎜ − η ⎟⎥ ⎠ ⎝ ⎠⎦ RT (7.14)

7.3.3 Parameters for Charge Transfer and Solid Electrolyte Conductivity

In order to validate the model and to estimate the unknown reaction rate constants and SE conductivity parameters, a series of experiments was conducted. The details of the experimental setup are given by Ye et al. (2004) and Ye (2006). The experimental data published by Ye et al. (2004) were used to determine the conductivity constant, CSE, and the activation enthalpy, E ASE, by a least square ﬁt of the modiﬁed Arrhenius-type equation (7.11). Table 7.2 lists the obtained parameter values; Figure 7.8 shows the experimental data and the simulated conductivity as a function of the inverse temperature. From these results, the value for the oxygen conductivity of the SE membrane between 0.04 and 0.24 S m−1 within the temperature range 450–550 °C is applied here in the modeling of butane oxidation. The maximal potential difference across the SE membrane is assumed to be 2.0 V, and therefore the highest molar oxygen ﬂuxes that can be reached are 0.5 and 3.0 mmol m−2 s−1, respectively.

Table 7.2 Model parameters for SE conductivity (7.11) and kinetic parameters for the

electrochemical reactions (7.14). Parameter

Value

Unit

CSE E ASE k0A k0C E AA C αA/C

2.8 × 108 96.9 × 103 1.46 × 103 1.46 × 104 200 × 103 0.3

S K m−1 J mol−1 mol m−2 s−1 mol m−2 s−1 J mol−1

7.3 Modeling of Solid Electrolyte Membrane Reactors

12

800

1100

650

550

450

T / [° C]

Range of operation

ln(σSET / [Sm−1K])

10 8 6 4 2 0 0.6

0.8

1 1000 T

1.2 −1

1.4

1.6

−1

/ [K ]

Figure 7.8 Modiﬁed Arrhenius plot of measured and simulated solid electrolyte conductivity. Reproduced from (Munder et al., 2005), reprinted with permission from Elsevier.

The characteristic isothermal current–voltage behavior obtained from oxygenpumping experiments (Ye et al., 2004) were used in order to determine the unknown kinetic parameters for the electrochemical reactions (7.12, 7.13). The experimental setup did not include a reference electrode and therefore the cathodic and the anodic charge transfer processes could not be measured separately. A value of 10 for the ratio of the cathodic to the anodic exchange current density and equal activation energies and charge transfer coefﬁcients were assumed. Under these assumptions, the parameters of Butler–Volmer kinetics, Equation 7.14, k0A C, E AA C , α A C, were determined by a least-square optimization using the SEMR model developed above. Figure 7.9 compares the calculated isothermal current–voltage behavior of the cell at 473 °C and 520 °C to the experimental data and Table 7.2 lists the obtained parameter values. At this point, some qualitative conclusions can be drawn. High voltages were necessary in the MA synthesis to attain a moderate current density (10–20 A m−2) along the reactor length. For comparison, in SOFCs operating at clearly higher temperatures, the current density might be two orders of magnitude higher. The main reason for the low current density is the low operating temperature, which has to be applied for the maleic anhydride synthesis in the SEMR but which leads to an exponential rise in both the SE membrane conduction resistance and the resistance of charge transfer reactions. Figure 7.9b shows the simulation of partial cell overvoltages at the operating temperature of 473 °C. It was found that not only SE ohmic resistance but also anodic and cathodic charge transfer reactions contributed signiﬁcantly to the voltage drop in the investigated system.

207

7 Solid Electrolyte Membrane Reactors (a) 1.5 Exp. results, T = 473 °C Model fit, T = 473 °C Exp. results, T = 520 °C Model fit, T = 520 °C

1 0.5

Ucell / [V]

0 −0.5 −1

−1.5 −2 −2.5 −3 0

20

40

60 Icell / [mA]

80

100

(b) 1.5 1

T = 473 °C

0.5

SE overvoltage ηSE

Open circuit cell potential

0 Ucell / [V]

208

−0.5 Anodic overvoltage ηA

−1

−1.5 −2 Cathodic overvoltage ηC

−2.5 −3 0

20

40

60 Icell / [mA]

Figure 7.9 Characteristic isothermal current-voltage behavior of the SEMR obtained from oxygen pumping experiments: a) at two different temperatures, and

80

100

b) analysis of partial cell overvoltages (geometrical surface area As = 23 cm2). Reproduced from Munder et al. (2005), reprinted with permission from Elsevier.

7.3 Modeling of Solid Electrolyte Membrane Reactors

7.3.4 Analysis of Maleic Anhydride Synthesis in Solid Electrolyte Membrane Reactor

The partial oxidation of n-butane to maleic anhydride (MA) is a complicated synthesis reaction, with the overall reaction given in Equation 7.15. C4H10 + 3.5 O2 ⎯VPO ⎯⎯ → C4H2O3 + 4 H2O

(7.15)

The VPO catalyst that promotes the above reaction (7.15) is vanadylpyrophosphate (VO)2P2O7, which to our knowledge does not exhibit electrocatalytic properties and which has very low electric conductivity (Rihko-Struckmann et al., 2006). Thus, as a ﬁrst approach it was assumed that the maleic anhydride synthesis in a SEMR takes place on the same route as in conventional catalytic reactors. Preceding molecular oxygen is released to the gas phase by the electrochemical charge transfer reaction as declared in the previous section. A simple Mars–van Krevelen type kinetic was assumed for the synthesis of MA. The reaction pathway is of the parallel-series type as shown in Figure 7.10. In detail, the selective formation of MA, Equation 7.16, as well as the butane and MA decomposition to COx, Equations 7.17 and 7.18, take place by consuming catalyst lattice oxygen. Only one active site, namely Catox is assumed to be active in the oxidation reactions (7.16–7.18) C4H10 + 7 Cat ox → C4H2O3 + 4 H2O + 7 Cat red

(7.16)

C4H10 + q2 Cat ox → 4 COx + 5H2O + q2 Cat red

(7.17)

C4H2O3 + q3 Cat ox → 4 COx + H2O + q3 Cat red

(7.18)

The reduced catalyst is afterwards re-oxidized by gaseous oxygen, Equation 7.19: Cat red + O2 → Cat ox

(7.19)

For reactions (7.16–7.19), rate expressions are derived according to the Mars–van Krevelen mechanism, Equation 7.20, assuming initially a quasi-steady-state for the intermediate lattice oxygen species, Catox, as well as a ﬁrst-kinetic order with respect to its concentration, xox. ⎛E ⎞ r j = k 0j exp ⎜ A ⎟ yHCx ox = k j yHC ⎝ RT ⎠ 1+ j

1

∑K j j

Figure 7.10

yHC yO2

Reaction scheme for the synthesis of maleic anhydride (MA).

(7.20)

209

210

7 Solid Electrolyte Membrane Reactors

However, such simple kinetics was not able to predict the experimental results and therefore it was necessary to further modify the model equations for MA synthesis. Retaining the assumed reaction mechanism, the Mars–van Krevelen type rate expressions given in Equation 7.20 for the reactions in Equations 7.16– 7.19 were modiﬁed by introducing reaction orders, βj, deviating from 1.0 with respect to the concentration of the oxygen species, xox, as shown in Equation 7.21. The assumption of a ﬁrst-order reaction with respect to the hydrocarbon species was kept as was suggested, for example, by Lorences et al. (2003) for low butane and MA concentrations. βj r j = k j yHCx ox

(7.21)

Furthermore, the quasi-steady-state assumption for the intermediate lattice oxygen species was adopted from the original Mars–van Krevelen approach, and the following implicit algebraic equation was added to the model equations: β2 β3 β1 + q2 ⋅ k2yBu x ox + q ⋅ k3yMA x ox k4 yO0.25 (1 − x ox )β 4 = 7 ⋅ k1yBu x ox 3 Catalyst reoxidation

MA formation

Butane total oxidation

(7.22)

MA total oxidation

With this modiﬁed kinetic approach, the differential selectivity for MA is given by: r −r SMA,diff ( z ) = 1 3 = r1 + r2

1−

k3 yMA ( z ) (β 3− β 1) (z ) x ox k1 yBu ( z ) k (β 2− β 1) (z ) 1 + 2 x ox k1

(7.23)

The results of steady-state butane oxidation experiments (Ye et al., 2004) were used to estimate the kinetic parameters. In order to reduce the number of adjustable parameters, the activation enthalpies, EA,j, for all reactions were initially adopted from Hess (2002). By ﬁtting the experimental reactor outlet concentrations of butane and maleic anhydride simultaneously for all experiments, the values for the remaining constants were determined. Table 7.3 summarizes the obtained parameters. Figure 7.11 shows the model predictions for butane conversion, MA selectivity and MA yield, together with experimental results as a function of the oxygen-to-butane feed ratio. Additionally, the selectivity curve for

Table 7.3 Kinetic parameters for the gas phase reactions in MA synthesis (7.16–7.19).

Reaction i (ri)

ki0 (kmol g−1 s−1)

i = 1 (7.16) i = 2 (7.17) i = 3 (7.18) i = 4 (7.19) a)

Adapted from (Hess, 2002).

0.512 8.605 227.5 10.0

EA,1 (kJ mol−1) 80.0a) 92.0a) 113.0a) 102.0a)

βi 0.71 1.03 0.48 1.0

7.3 Modeling of Solid Electrolyte Membrane Reactors (a) 50 Exp. Butane Conversion Model fit

Butane Conversion / [%]

45 40 35 30 25 20 15 10 5 0 0

0.5

1

1.5

2

2.5

Feed Ratio O2/Butane / [mol O2/mol C4] (b) 100 Exp. MA Selectivity Model fit Exp. COx Selectivity Model fit

MA and COx Selectivity / [%]

90 80 70 60 50 40 30 20 10 0 0

0.5

1

1.5

2

2.5

Feed Ratio O2/Butane / [mol O2/mol C4] (c)

15

MA Yield / [%]

Exp. MA Yield Model fit

10

5

0 0

0.5

1

1.5

2

2.5

Feed Ratio O2/Butane / [mol O2/mol C4]

Figure 7.11 Experimental and simulated results as function of the oxygen-to-butane feed 0 = 0.0056, MCat = 165 mg). Reproduced from Munder ratio (T = 480 °C, V˙ A,0 = 32 ml min−1, y Bu et al. (2005), reprinted with permission from Elsevier.

211

212

7 Solid Electrolyte Membrane Reactors

COx, which was calculated assuming the carbon balance to be completely fulﬁlled, is added to Figure 7.11b and compared with measured results. Generally, the simulations agreed well with the experimentally determined butane conversion and MA yield. The increasing butane conversion and, as a result, the increasing MA yield for rising oxygen-to-butane feed ratios up to 1.4 are well reproduced. However, there is a notable difference between measured and simulated selectivity to MA and COx for oxygen-to-butane feed ratios below 0.5. The decline of the integral MA selectivity for low oxygen-to-butane feed ratios could not be reproduced by the model, as seen in Figure 7.11. Both a more detailed description of the mass transfer in the catalyst layer (1-D + 1-D) and the implementation of the transient kinetics presented by Huang et al. (2002) with re-estimated parameters provided an excellent basis for further analysis of the system (Munder, Rihko-Struckmann, and Sundmacher, 2007). By extending the Huang model with two reactions: (a) the adsorption of carbon species at reduced VPO lattice and (b) the subseqent oxidation of the species: 9 C4H10 + ( L ) ⎯r⎯ → C4 ( L )

(7.24)

→ 4 COx + 5H2O + ( L ) + q (S) C4 ( L ) + q O (S) ⎯⎯⎯

(7.25)

r10 ,11

the model predictions could be improved, especially for the co-feed conditions. 7.3.5 Analysis of Oxidative Dehydrogenation of Ethane in a Solid Electrolyte Packed-Bed Membrane Reactor

The oxidative dehydrogenation of ethane has been discussed extensive in the previous Chapters. In the present Chapter 7 we discuss the characteristics of carrying out the reaction in a solid electrolyte packed-bed membrane reactor. In the analysis, the basic reactor model including the electron transfer reactions and the ion transfer in the electrolyte as presented above for the electrochemical synthesis of MA was applied also here for the oxidative dehydrogenation of ethane (ODHE) with a VOx/γ-Al2O3 catalyst (Chalakov et al., 2007). However, in the present ODHE studies the catalyst particles were placed in a packed-bed solid electrolyte membrane reactor and not ﬁxed with the electrode, as in the example of MA synthesis. The charge transfer reactions – oxygen reduction to ions and the release of gaseous dioxygen on the anode, as well as ion conduction – are comparable to those presented in the previous chapter for MA synthesis. The pseudohomogeneous, one-dimensional approach for the anodic catalyst layer is fully applicable here. In the reaction network (see Chapter 3, Figure 3.1) ethane reacts in two parallel pathways to ethylene and CO2 by Equations 3.1 and 3.2. Furthermore, the formed ethylene can be oxidized by two parallel pathways to CO or CO2 according to Equations 3.3 and 3.4. and the consecutive CO to CO2 according Equation 3.5. The kinetic model for the oxidative dehydrogenation of ethane originally proposed by Klose et al. (2004) and presented in Chapter 3 is applied

7.3 Modeling of Solid Electrolyte Membrane Reactors

here also for heterogeneously catalyzed reactions, because it is based on measurements with the same VOx/γ-Al2O3 catalyst at the same temperature range as applied in our experiments. The Mars–van Krevelen mechanism is assumed as well here for the dehydrogenation step, in which ethane reacts with lattice oxygen to form ethylene. The total oxidation of ethane and ethylene (3.2–3.4) is assumed to occur only in the presence of gaseous oxygen by the Langmuir–Hinshelwood mechanism, assuming non-competitive adsorption of the reactants. The last reaction (3.5) in the network is described by a Langmuir–Hinshelwood mechanism with competitive adsorption of the reactants. According to the model presented by Klose et al. (2004) it was assumed that oxygen participates in all reactions in a dissociated form giving in the kinetic equations the reaction order of 0.5 for oxygen whereas for all other compounds the reaction order is one. As discussed above for the MA synthesis, the equations of the electrochemical operation (the charge transfer reactions of oxygen on the cathode and the anode by Butler–Volmer kinetics, Equations 7.12– 7.14) are included here as well in the OHDE model. In the experimental investigation of ODHE was found that the ethylene selectivity was not positively inﬂuenced in the solid electrolyte membrane reactor operation compared to the packed-bed membrane reactor operation (Chalakov et al., 2007). The selectivity ratio SCO2 SCO was found to depend on the type of oxygen supply, so that with a gaseous oxygen supply the ratio was always lower than that with an electrochemically supplied oxygen. The model presented in Chapter 3 (Table 3.3) with the parameter values from Table 3.4 was not directly able to predict the obtained results in co-feed mode. A re-estimation for the parameters in the non-electrochemical reactions was necessary in order to decribe the experimental results for OHD of ethane in the membrane reactor operated in the co-feed mode. After this re-estimation, the conversion, yield and COx selectivities were well predicted in co-feed condition without electrochemically supplied oxygen. However, the model applicability was still limited for conditions in oxygen pumping mode (electrochemical supply). The model, including the equations for charge transfer reactions of oxygen on the cathode and the anode (7.12–7.14), was not able to predict the experimental results of the EMR operation conditions with electrochemically supplied oxygen. One reason for the discrepancies between the experimental data and the simulated was concuded to be the additional electrochemically induced side reactions, as suggested already by Chalakov et al. (2007), Ye et al. (2004) and Ye et al. (2005). In contrary to the co-feed mode, where the oxygen on the anode exists only in form of gaseous O2, additional oxygen species, e.g., O2−, O2− , O22− , O−, O (adsorbed) might be present in EMR operation during the electrochemical pumping. Therefore the model was completed ﬁnally by implementing two electrochemical side reactions into the reaction network. The charged oxygen species are likely highly active in oxidation reactions, as concluded by Chalakov et al. (2007) and therefore two further reactions were added to the model describing the ethylene reaction with O2− either to CO (7.26) or CO2 (7.27) according to equations:

213

214

7 Solid Electrolyte Membrane Reactors Table 7.4 Kinetic equations for the electrochemical reactions in the electrochemically

supported oxidative dehydrogenation of ethane. Reaction

Equation

α F relCO = kelCO ⎡⎢exp ⎛⎜ a ΔΦ A ⎞⎟ ⎤⎥ y CA2H4 ⎝ RT ⎠⎦ ⎣ α aAF ⎛ CO2 CO2 ⎡ rel = kel ⎢exp ⎜ ΔΦ A ⎞⎟ ⎤⎥ y CA2H4 ⎝ RT ⎠⎦ ⎣ C C E α F α CF relC = k0Cexp ⎛⎜ − A ⎞⎟ ⎡⎢exp ⎛⎜ a ΔΦ C ⎞⎟ − ( y O2 )0.5 exp ⎛⎜ − c ΔΦ C ⎞⎟ ⎤⎥ ⎝ RT ⎠⎦ ⎠ ⎝ RT ⎠ ⎣ ⎝ RT A A A E F F α α relA = k0A exp ⎛⎜ − A ⎞⎟ ⎡⎢exp ⎛⎜ a ΔΦ A ⎞⎟ − ( y O2 )0.5 exp ⎛⎜ − c ΔΦ A ⎞⎟ ⎤⎥ ⎝ RT ⎠⎦ ⎠ ⎝ RT ⎠ ⎣ ⎝ RT A

3el 4el 6 7

C2H4 + 4 O2 − → 2 CO + 8 e − + 2 H2O

(7.26)

C2H4 + 6 O2 − → 2 CO2 + 12 e − + 2 H2O

(7.27)

The backward reactions were assumed to be unlikely and therefore the kinetics of the reactions in Equations 7.26 and 7.27 were described by the simple Tafel equation. The kinetic equations for the electrochemical charge transfer and side reactions (7.14, 7.26, 7.27) are summarised in Table 7.4 and all parameter values in Table 7.5. The kinetic equations for the heterogeneously catalyzed gas phase reactions were taken directly from Table 3.3. The model predictions calculated with this extended model, including the electrochemical side reactions, are presented on Figure 7.12. After the implementation of the additional electrochemical reactions (7.26 and 7.27), the model simulations agreed well with the experimental results. The selectivities towards the three products and the ethylene yield were well predicted with the extended model. Due to the oxygen-consuming, competing electrochemical side reactions, the reaction with ethane is depressed to some extent. As seen in the examples of the maleic anhydride synthesis and the oxidative dehydrogenation of ethane in solid electrolyte membrane reactors, conventional reaction models and the equations which are presented in literature are usually not directly applicable to conditions where reagents are supplied electrochemically. The models describing solid electrolyte membrane systems become more complex as the electrochemical aspects have to be included. The kinetic equations for charge transfer reactions of the reagents on the cathode and the anode described by Buttler–Volmer equations have to be included in the model. The charge balances characterizing the anodic and the cathodic potential difference across the interfaces between the electrolyte and the electrodes have to be taken into consideration. The ohmic potential loss in the electrolyte and in the electrodes is described by the corresponding equations, and the temperature

7.3 Modeling of Solid Electrolyte Membrane Reactors

215

Table 7.5 Kinetic parameters for the gas phase reactions in oxidative dehydrogenation of ethane (Equations in Table 7.4).

EA,i (kJ mol−1)

k0i

Ox Red

94 1.9 × 103 (mol kg−1 s−1) 1.7 × 103 (mol0.5 m1.5 kg−1 s−1)

Reaction i (ri)

k0i (mol kg−1 s−1)

EA,i (kJ mol−1)

i=2 i=3 i=4 i=5

4.4·× 103 19.6 0.3 45.1 × 103

114 51 51 118

Electrochemical reactions

k0i (mol m−2 s−1)

EA,i (kJ mol−1)

α aA cC

i = 3 el i = 4 el C (reaction 6) A (reaction 7)

1.1 × 10−2 0.9 × 10−2 1.46 × 103 1.46 × 104

220 180 130 130

0.3 0.3 0.3 0.3

0.60

0.80 S-C2H4 Experiment S-C2H4 Model fit S-CO Experiment S-CO Model fit S-CO2 Experiment S-CO2 Model fit

0.50 0.60

0.40

Selectivity [%]

Ethane Conversion and Ethylene Yield [%]

Reaction

X-C2H6 Experiment X-C2H6 Model fit Y-C2H4 Experiment Y-C2H4 Model fit

0.30 0.20

0.40

0.20

0.10 0.00

0.00

0.0

0.5

1.0

1.5

2.0

2.5

Feed Ratio O2/C2H6 [mol/mol]

Figure 7.12 Experimentally obtained and model predicted ethane conversion, ethylene yield and selectivities as a function of the oxygen-to-ethane feed ratio during EMR operation (T = 580 °C; MCat/V˙ = 0.013 g

3.0

0.0

0.5

1.0

1.5

2.0

Feed Ratio O2/C2H6 [mol/mol]

min−1 cm−3). The predictions with the extended model include the additional electrochemical side reactions. Reproduced from (Chalakov et al., 2009), reprinted with permission from Elsevier.

2.5

3.0

216

7 Solid Electrolyte Membrane Reactors

dependence of the electrolyte conductivity is described by modiﬁed Arrhenius type equations. The overall cell potential might be calculated according to Kirchoff’s law. As clearly seen in the both examples, additonal electrochemical reactions are likely occuring in the reaction system where one reagent is supplied electrochemically. The existence of more active reagent species on the electrode is difﬁcult to conﬁrm experimentally, but they are likely and the reactions due to these species are to be considered in the model. However, the engineering approaches as presented here in the above examples and in the cited publications (Munder et al., 2005; Munder, Rihko-Struckmann, and Sundmacher, 2007; Chalakov et al., 2007) including both the electrochemical and heterogeneously catalyzed reactions as well as the reaction engineering aspects are to date rare in the literature, but are necessary for determining the optimal operation conditions in such complex systems.

7.4 Membrane Reactors Applying Ion-Conducting Materials

In the last part of this chapter some examples of various systems are given where, according to the literature, either proton or oxygen ion-conducting materials have been used as a membrane electrolyte. When one considers ﬁnancial funding, most resources have been focused on the development of fuel cells. Due to the abundant amount of publications – review articles as well as books describing the recent development of different kind of fuel cells (Larminie and Dicks, 2003; Srinivasan, 2006; Basu, 2007; Spiegel, 2007; Barbir, 2005) – we discuss here the aspects of fuel cells only brieﬂy. 7.4.1 High-Temperature Oxygen Ion Conductors 7.4.1.1 Solid Oxide Fuel Cell for Electrical Energy Production A technology which uses oxygen ion-conducting membranes semi-commercially is the solid oxide fuel cell (SOFC) for electrical energy production. Electrochemical energy conversion can be carried out highly efﬁciently in solid oxide fuel cells. The most valuable beneﬁts of SOFC technology compared to the other fuel cells are that a wide variety of fuels can be processed and the catalyst tolarates sulfur due to the high operating temperatures (>800 °C). A signiﬁcant beneﬁt is also the high achievable electrical net efﬁciency, which for small 1 kW units is about 50%; for large pressurized SOFC/gas turbine systems, electrical efﬁciencies greater than 65% are expected (Weber and Ivers-Tiffée, 2004; Williams, 2007). The developers of SOFC technology among others are Siemens–Westinghaus with the 250 kW multi-tubular units, Rolls–Royce with a segmented series arrangement of individual cells (Gardner et al., 2000), Allied–Signal Aerospace Company with the monolith concept (Larminie and Dicks, 2003) and a joint venture company Staxera (2009) and Hexis (2009) with planar technology providing sophisticated

7.4 Membrane Reactors Applying Ion-Conducting Materials

heat management with integrated indirect reforming. So far the development of SOFC has concentrated mostly on stationary units, but a new, attractive ﬁeld for this technology is SOFC-based auxiliary power units (APU) for mobile applications (Pfafferodt et al., 2005; Grube, Hohlein, and Menzer, 2007). Regardless of the present success of pilot tests with pre-commercial SOFC units, there still exist severe challenges of the SOFC technologies. The present high operating temperature results in many inherent problems, such as low long-term stability of the materials, cell degradation due to mechanical stress, electrode sintering and slow start-up. The thermal expansion coefﬁcients of the fuel cell components – electrolyte, electrode layers and interconnections – have to match well with each other, otherwise the thermal stress causes delamination at the unit interfaces or cracking of the electrolyte. At the prevailing temperature further demands are high chemical compatibility and stability, as discussed in detail in the review by Weber and Ivers-Tiffée (2004). Increased long-term stability and a decrease in system cost would be possible, if the development of low or intermediate temperature SOFC technologies (600–800 °C) is successful in the near future. One idea in the ﬁeld of SOFC technology based on the oxidation of hydrocarbons deviates from the strict separation of fuel and oxidant (Hibino et al., 2000a, 2002b; Yano et al., 2007; Buergler, Grundy, and Gauckler, 2006). The working principle of the single chamber cell is based on the highly selective catalytic activity of the electrodes. The criteria for the electrodes are: (a) one electrode has to be electrochemically active for the oxidation of the fuel but should be inert to oxygen reduction, (b) the other electrode (cathode) should be highly active for the reduction of oxygen but inert in the oxidation reaction. High concentrations of the partial oxidation products, hydrogen and CO, cover the immediate vicinity of the anodic electrode and lead the electrochemical oxidation of these gases. At present, ideally selective anode and cathode materials for fuel oxidation and oxygen reduction are yet not available for single cell fuel cells, and further efforts are needed to realize these. The energy conversion efﬁciency of such systems is still low, due to the large amount of unreacted fuel. 7.4.1.2 Oxidative Coupling of Methane to C2 and Syngas from Methane The conversion of methane into higher hydrocarbons, such as the C2 coupled products, ethane and ethylene, or syngas production by partial oxidation, has signiﬁcant commercial importance. Methane is an abundant natural resource, but its direct transport is not highly economical and its conversion to upgraded products is highly challenging. Recent reviews cover the research on methane coupling and hydrogen production in the past 20 years with the use of solid electrolyte membane reaction appyling either O2−, H+ or MIEC (O2−, e−) electrolytes (Athanassiou et al., 2007; Stoukides, 2000). The option of using solid oxide membranes for supplying the necessary oxygen for methane activation has several economical and environmental advantages over the direct use of air as oxidant. The membrane is impermeable to nitrogen providing only oxygen for the reactions, thus avoiding NOx formation. In addition, in a solid electrolyte process, there are the combined

217

218

7 Solid Electrolyte Membrane Reactors

possibilities of electrochemical enhancement of products selectivity, simultaneous generation of electrical power and, in general, more control over the reaction pathway. In the electrocatalytic partial oxidation of methane to synthesis gas in a SE membrane reactor, the methane feed stream does not contain oxygen. It is transferred directly into the reaction zone through the membrane by passing an anodic current through the cell. The electrocatalytic oxidation of methane has been intensively investigated both in co-generation mode as well as in oxygen pumping conditions with various catalysts (Athanassiou et al., 2007). The main advantage in such systems is that the SE membrane prevents the reaction mixture from explosion, since CH4 and O2 (air) are separated by the YSZ electrolyte. Research has been focused also towards the production of partially oxidized higher hydrocarbons, e.g., ethane, propane and propene (Takehira et al., 2002, 2004; Hellgardt, Cumming, and Al-Musa, 2005), as well as butane as detailed above (Ye et al., 2004, 2006). Under oxygen-pumping conditions with MoO3 as catalyst, the evolution of gaseous oxygen was observed in the operation with alkanes (Takehira et al., 2004). Alkenes were more active and they were oxidized with high selectivity without oxygen evolution. Ethane and propane were found to be inert in a cell conﬁguration MoO3/Au|YSZ|Ag, while isobutane was partially oxidized to methacrolein. The highest selectivity (73%) was obtained for methacrolein from isobutene. In a comparison of experiments using V2O5 as catalyst in the same cell under oxygen-pumping conditions, both alkanes and alkenes were oxidized. Isobutane was oxidized to methacrolein with low selectivity, and propane formed propene by oxidative hydrogenation. Ethane was slowly oxidized to CO2. With V2O5 as catalyst the evolution of gaseous oxygen was observed in all reactions. 7.4.1.3 Dry Reforming of Methane The dry reforming of methane with CO2 provides the possibility to enhance natural gas utilization and to convert the carbon resources inherently contained in CO2 and CH4 into synthesis gas. Besides of the most conventional steam reforming of methane for hydrogen production, there are hundereds of publications concerning the catalytic aspects of dry reforming. The reforming of CH4 by CO2 in a solid electrolyte membrane reactor has some advantages over catalytic reforming. Catalyst deactivation by coking is the most severe limitation of the process, and it can be suppressed to some extent by the oxygen ions being directly supplied to the catalyst being ﬁxed on the electrode layer of the SE membrane. The effect of electrochemically supplied oxygen in the reforming of CH4 with CO2 have been investigated, among others, by Belyaev et al. (1998) and by Moon and Ryu (2003) in a Pt|YSZ|Pt or a NiO–MgO|YSZ|(La,Sr)MnO3 cell, respectively. During oxygen pumping conditions, the system stability was improved as the catalyst stability was increased by electrochemically supplied oxygen to the anodic catalyst layer. The observed current was generated with the reactions of the electrochemically supplied oxygen with CH4, CO, H2 or surface carbon formed during the internal reforming of CO2.

7.4 Membrane Reactors Applying Ion-Conducting Materials

7.4.2 High-Temperature Proton Conductors

A typical proton-conducting ceramic material such as SrCe0.95Yb0.05O3-α is a solid solution based on the perovskite-type oxide SrCeO3, in which Ce is partly replaced by Yb. Other perovskite-type oxides – based on SrCeO3 or BaCeO3 – in which some trivalent cations are partially substituting cerium, show protonic conductivity, too. The general formulas are SrCe1-xMxO3-α or BaCe1-xMxO3-α where M stands for a certain rare earth element, x is less than its upper limit of solid solution formation range (usually less than 0.2) and α represents the oxygen deﬁciency per unit formula. The ceramics of these perovskite-type oxide solid solutions exhibit p-type electronic (hole) conduction under oxidizing atmosphere free of hydrogen or water vapor at high temperatures (Iwahara et al., 2004). Proton conductivity of these oxides can be obtained if protonic defects exist. There are two mechanisms for proton conduction. The ﬁrst is the Grotthus mechanism, in which the proton jumps between adjacent oxygen ions. The second mechanism is hydroxyl ion migration, also called the “vehicle” mechanism. Protonic defects can be formed by reaction between water molecules and oxygen vacancies according to the equation: OOx + VOii + ⋅ H2O ( g ) → 2 OHOi

(7.28)

where two effectively positive hydroxyl groups on regular oxygen positions are formed. Another important mechanism forming protonic defects is the reaction of hydrogen with electron holes according to: 2 h i + 2 OOx + H2 → 2 OHOi

(7.29)

for which the presence of excess holes is obviously necessary. The conductivities in hydrogen atmosphere are in the order of 10−3–10−2 S cm−1 at 600–1000 °C. Proton conduction has been measured by electrochemical hydrogen transport experiments in hydrogen- or water vapor-containing atmosphere. The role of water vapor can be seen in Figure 7.13 (Matsumoto et al., 2001). It was found that the hydrogen evolution rate obeyed Faraday’s law up to very high current densities, using humidiﬁed cathode carrier gases. Within the examined range of water vapor pressures, 6.6 × 102 to 2.3 × 103 Pa, the current efﬁciency was almost unity until current densities of 450–600 mA cm−2 were reached, which was about ten times larger than in the operating case where dry carrier gas was used. A high-temperature proton-conducting membrane can be used in various applications, as a sensor of hydrogen or hydrocarbons, for the separation of hydrogen, energy conversion and the synthesis of chemicals, as discussed brieﬂy in the following sections. Recent studies also clarify the opportunitities of using proton conductors for nuclear fusion process, where hydrogen isotopes (deuterium and tritium) must be extracted from reactor core exhaust gas containing He and other elements (Iwahara et al., 2004).

219

7 Solid Electrolyte Membrane Reactors H2 (pH2O = 2.3 × 103 Pa), Pt|SrCe0.95Yb0.05O3-δ|Pt, Ar(wet) Theoretical

SrCe0.95Yb0.05O3

Hydrogen evolution rate / μmol min-1 cm-2

220

T=800°C pH 0=2.3 kPa 2

pH 0=1.4 kPa 2

pH 0=0.66 kPa 2

Cathode wet

Dry hydrogen atmosphere

Current density / mA cm-2

Figure 7.13 Hydrogen pumping using proton-conducting ceramic: H2 evolution rate at cathode versus cell current density. Reproduced from (Matsumoto et al., 2001), reprinted with permission from the Electrochemical Society.

eR

H2

pH2(A)

H2 H+

pH2(C)

Figure 7.14 Working principle of hydrogen concentration cell using a proton-conducting membrane.

7.4.2.1 Hydrogen Sensors and Pumps In the open circuit mode (OCM), proton-conducting electrolyte membranes can be used to detect hydrogen, steam, alcohol or hydrocarbons (e.g., a leak detector for chemical plants or coal mines). The working principle of a sensor with protonconducting membrane is based on the principle of the electrochemical hydrogen concentration cell (see Figure 7.14) where the theoretical open circuit cell voltage (OCV) is E0cell ∼ ln [PH2 ( A ) PH2 (C)] , where PH2(A) and PH2(C) are the partial pres-

7.4 Membrane Reactors Applying Ion-Conducting Materials

sures of hydrogen in each electrode compartment. Therefore, the OCV can be used as a signal for hydrogen activity if PH2(A) or PH2(C) is known. For hydrocarbon or alcohol sensors both single- and two-chamber constructions are possible (Iwahara et al., 2004). In the single-chamber sensor, the electrodes possess different activity. Only one electrode is active for hydrocarbon oxidation in air. Therefore, the separation of electrode compartments is not necessary and no standard gas is needed, which are the major advantages of this sensor variant. As a further application of proton-conducting membranes, hydrogen can be selectively separated from gas mixtures, for example, containing compounds such as water and hydrogen disulﬁde, by proton pumping at close-circuit conditions. 7.4.2.2 Fuel Cells During the past two decades, researchers in the ﬁeld of solid oxide fuel cells paid much attention to the preparation and characterization of solid oxide materials with protonic conductivity (Grover Coors, 2003; Hassan, Janes, and Clasen, 2003; Fehringer et al., 2004; Taherparvar et al., 2003). Historically, one of ﬁrst works on high-temperature proton-conducting fuel cells was published by Iwahara et al. (1981). The interest in protonic conductors and their utilization in fuel cells is high because complete hydrogen utilization could easily be attained in a SOFC based on a protonic electrolyte. Protonic ceramic fuel cells are targeted for operation at 55– 65% electrical efﬁciency with pipeline natural gas as feed. This can only be achieved with greater than 90% direct methane fuel utilization. Such high fuel utilization is made possible by two major factors. First, high thermochemical efﬁciency of reforming and water shift reactions at the anode is possible at the high operating temperatures of 700–800 °C. Second, water vapor is produced at the cathode where it is subsequently swept away by the air ﬂow, rather than at the anode where it would dilute the fuel (carbon dioxide is the only anode exhaust gas). 7.4.2.3 Electrocatalytic Membrane Reactors Moreover, proton-conducting membranes are applicable in electrocatalytic reactors for hydrogenations and dehydrogenations of organic compounds, methane activation, steam electrolysis, water gas shift, ammonia reactions as listed in the review by Kokkoﬁtis et al. (2007). Several reactor concepts are illustrated in Figure 7.15. Unique features of proton-conducting membrane reactor concepts compared to traditional catalytic reactors are:

• • •

hydrogen and the compounds to be hydrogenated or dehydrogenated are kept separated by the membrane, the chemical potential of hydrogen at the reaction sites and the reaction rate can be controlled via the electrode potential or via the electric current, hydrogenation and dehydrogenation of organic compounds on either side of the membrane can be carried out simultaneously in a single unit.

In the methane coupling, the formation of ethane and ethylene was enhanced by applying an electric potential difference to the reactor (Hamakawa, Hibino, and

221

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7 Solid Electrolyte Membrane Reactors

C=C

H2

C-C H+

H+ C-C

Dehydrogenation

Hydrogenation

CH4

O2

H2O H+

H+ H2O C2

H2

C=C

O2

Methane Coupling

H2 Steam Electrolyzer

Figure 7.15 Examples for the use of proton-conducting membranes in electrocatalytic membranes reactors. Reproduced from (Sundmacher, Rihko-Struckmann, and Galvita, 2005), reprinted with permission from Elsevier.

Iwahara, 1993). Another application was the reduction of NO occurring in automobile exhaust lines (Kobayashi et al., 2002). The reduction of NO by hydrogen, which was produced by a steam electrolysis cell, was tested with different catalysts on the cathode side. A mixture of Pt-sponge and Sr/Al2O3 was found to be the most active catalyst for the preferred reduction of NO in excess of O2. Recently, the hydrogenation of CO2 was demonstrated successfully with proton-conducting membranes strontia–zirconia–yttria perovskite and the working (cathodic) electrode was a polycrystalline copper ﬁlm (Karagiannakis, Zisekas, and Stoukides, 2003). The observed reaction rates are about one order of magnitude higher than under normal catalytic conditions, when hydrogen is supplied electrochemically. Recently proposed application of a high-temperature proton-conducting membrane is the dehydrogenation of propane over Pt and Pd to produce propylene and hydrogen (Karagiannakis, Kokkoﬁtis, and Zisekas, 2005). 7.4.3 Low-Temperature Proton Conductors

The most established low-temperature proton conductor is the polymer electrolyte membrane (PEM) material Naﬁon, which is commercially available from DuPont. This membrane is a fully ﬂuorinated polymer-ether backbone having sulfonic acid groups. After solvatization of the acid groups with water, the PEM exhibits protonic conductivity. Due to the necessity of humidiﬁcation and due to limitations regarding maximum operating temperatures (<120 °C) of Naﬁon-type materials, intense research activities aim to develop new proton conductors. The operation of PEM-based reactors, especially fuel cells in transportation, would be

7.4 Membrane Reactors Applying Ion-Conducting Materials

clearly simpliﬁed if the membranes could work without any humidiﬁcation up to temperatures 200 °C. A promising material being suitable for higher temperatures is polybenzimidazole (PBI) (He et al., 2007; Li et al., 2004). The humidiﬁcation-free operation of PBI membranes at higher temperatures allows a higher CO concentration in hydrogen fuel cells (PEMFC) fed with reformate gas because at higher temperatures CO adsorption at the anode catalyst (Pt) is of less importance. Other possible membranes for PEM fuel cells are polymer– ceramic composite protonic conductors (Savadogo, 2004; Alberti and Casciola, 2003) and polyaromatic polyheterocyclic materials such as polysulfones (PSU), polyethersulfone (PES), polyetherketone (PEK), polyetheretherketone (PEEK) and polyphenyl quinoxaline (PPQ) (Roziere and Jones, 2003). The latter materials have to be doped with appropriate acids to achieve the desired proton conductivity. 7.4.3.1 PEM Fuel Cells Today, PEM materials are used as low-temperature proton-conducting membranes in energy conversion where the total oxidation of the fuel with maximal electrical energy production is the primary goal. The applications of low-temperature fuel cells have reached semi-commercial stage and several test units have been launched to the market. The operation of low-temperature proton-conducting membrane fuel cell using hydrogen as feed is effective, and high current densities can be reached. However, the use of gaseous hydrogen as a feed brings many logistic and safety problems to solve and therefore research efforts have been focused over several decades to develop safe storage and transportation systems for various forms of hydrogen. Due to the mentioned difﬁculties in the operation of hydrogen fuel cell, a competitive fuel cell technology operating at low temperature is the direct methanol fuel cell (DMFC), where a liquid methanol–water solution is directly used as the anode feed. Handling liquid methanol is less complicated than handling gaseous hydrogen, and therefore the DMFC is a very promising low-temperature fuel cell technology, especially for transportation applications. The working principle of this fuel cell is presented in Figure 7.16. A review by Schultz, Zhou, and Sundmacher (2001) discussed the status and trends of DMFC technology in detail. A detailed analysis of the kinetic aspects of the electrochemical oxidation of methanol were carried out by Vidakovic, Christov, and Sundmacher (2005); Vidakovic et al. (2007); and Krewer et al. (2006). A severe limitation of DMFC operation is caused by deactivation of the anodic electrode catalyst (Pt/Ru) due to the irreversible adsorption of the reaction intermediate CO on catalyst active sites. Another limitation comes from the undesired transport of methanol from the anodic compartment through the membrane to the cathodic side (methanol cross-over). Cross-over and the direct oxidation of methanol on the cathode lead to a reduced cathode potential and thereby to a reduced overall cell voltage. A detailed mathematical analysis of methanol cross-over and the transport mechanisms in PEM was reported by Sundmacher et al. (2001) and Schultz et al. (2007).

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7 Solid Electrolyte Membrane Reactors Pt/Ru

Anode: CH3OH(l) + H2O(l) Cathode: 3/2 O2(g) + 6 H+ + 6 e- Pt

CO2(g) + 6 H+ + 6 e3 H2O(l)

Overall: CH3OH(l) + 3/2 O2(g)

CO2(g) + 2 H2O(l)

Catalyst layers (10-40 μm)

CH3OH / H2O / CO2

U0cell = 1.21 V

O2-reduced air / H2O / CO2

H2O

e-

eH+ Anode Bipolar Plate (Electric contact + reactant supply) CH3OH / H2O

Cathode CH3OH

T = 50 - 110 °C p = 0.1 - 0.4 MPa

PEM (20-200 μm) Air Diffusion layers (100-200 μm)

Figure 7.16 Working principle of direct methanol fuel cell (DMFC). Reproduced from (Sundmacher, Rihko-Struckmann, and Galvita, 2005), reprinted with permission from Elsevier.

7.4.3.2 Proton Exchange Membrane Reactors The application of polymeric proton exchange membranes (PEM) in chemical reactors at low temperatures (<120 °C) is not common. Only a few examples of such PEM reactors – operated in electrolysis mode or in fuel cell mode – can be found in the open literature. Theoretically these reactors can be used for speciﬁc oxidation, dehydrogenation and hydrogenation reactions, as some interesting examples in the literature show. The operating modes of these reactors depend on the reactions applied. In an optimal case, the co-generation of electrical energy and valuable chemical products has been successful. Figure 7.17a,b present schematic illustrations of PEM reactor conﬁgurations which are discussed in more detail in the following. Electrolysis Operating Mode The oxidation of various aliphatic alcohols with oxygen produced by in situ water electrolysis can be taken as an example of electrolysis carried out in a polymer electrolyte membrane reactor (Simond and Comninellis, 1997). Water was fed together with the various aliphatic alcohols to the anodic side of Naﬁon 117 membrane reactor, where IrO2 deposited on the porous titanium layer worked as anode. The hydroxyl radicals formed in the electrolysis were interacting with the anode forming the higher oxide IrO3, which was either reactive in the alcohol oxidation or evolved gaseous oxygen in the catalyst redox reaction (IrO3/IrO2). The tested alcohols showed remarkable differences in

7.4 Membrane Reactors Applying Ion-Conducting Materials

225

(a) Dehydrogenation

e

Hydrogenation

e-

-

RuO2 | Nafion | Pd, 60°C (adopted from [2])

Oil (soybean Alcohol + H2O (Isopropanol)

H Oxidized Products (Aceton)

H2O

Ir | Nafion | Pt, 20°C (adopted from [1])

+

H+

Hydrogenated Oil

O2

H2

Rh-Pt | Nafion | Rh-Pt, 25-70°C (adopted from [3])

1

[Simond and Comninellis, 1997], 2[An et al., 1999], 3[Itoh et al., 2000]

(b)

Hydrogenation

Dehydrogenation e-

R Methanol (+ H2O)

e-

Pt | Nafion | Pt , 25°C (adopted from [4])

NO2

Pt/C|Nafion| Pt/C 15-70°C (adopted from [6])

R NH2

O2 +

NH2

H+

H Methylformat Dimethoxymethane

H2O H2

Ir⏐H3PO4/silica wool⏐Pt, 70-100°C (adopted from [5])

CH2=CHCH2OH CH3CH2CH2OH

Pt/C|Nafion| Pt/C 15-70°C (adopted from [7])

[Yamanaka and Otsuka, 1988], 5[Otsuka et al.. 2003], 6[Yuan et al., 2001], 7[Yuan et al., 2003]

4

Figure 7.17 a) Proton exchange membrane (PEM) reactors: examples for electrolysis operating modus. Reproduced from (Sundmacher, Rihko-Struckmann, and Galvita, 2005), reprinted with permission from Elsevier. b) Proton exchange membrane

(PEM) reactors: examples for fuel cell operating modus. Reproduced from (Sundmacher, Rihko-Struckmann, and Galvita, 2005), reprinted with permission from Elsevier.

reactivities, secondary alcohol, isopropanol being the most reactive, followed by ethanol and methanol, with n-propanol having clearly the lowest reactivity. The electrolysis of water can be applied also in hydrogenation reactions, as two examples show: the hydrogenation of benzene (Itoh et al., 2000) or soybean oil (An et al., 1999; An, Hong, and Pintauro, 1998). In both systems, the electrolysis of water was carried out on the anode, where O2 and H+ were formed electrochemically. Protons migrated through the membrane, and on the cathode either atomic or molecular hydrogen was consumed for hydrogenations. Initially electrochemical and non-electrochemical hydrogenation of benzene (co-feed) were compared

226

7 Solid Electrolyte Membrane Reactors (b)

% C18:0 + trans

Chemical hydrogenation with Ni catalyst

Power consumption (kW-h/kg)

(a)

Water Anode Feed

H2 Anode Feed

PEM reactor with H2 and a Pd-black cathode

Current Density (A/cm2)

Soybean Oil IV Figure 7.18 a) Comparison of reactor type (PEM reactor with Pd black cathode versus chemical hydrogenation with Ni) in soybean oil hydrogenation. Reprinted with permission from (Pintauro et al., 2005). Copyright American Chemical Society. b) Dependence

of the PEM reactor power consumption from the anode feed (H2O vs H2) for partially hydrogenated soybean oil. Reprinted with permission from (Pintauro et al., 2005). Copyright American Chemical Society.

when hydrogen was pumped as protons through the membrane, and it was evident that the production rate of cyclohexane was much higher during solid electrochemical operation. The direct electrochemical pumping of hydrogen in a PEM was applied for the selective hydrogenation of soybean oil (Pintauro et al., 2005). In the partially hydrogenated oil product, the nutrition quality of the product was improved by PEM reactor processing, as a lower percentage of trans-fatty acid isomers and saturated stearic acids was detected in the product oil after hydrogenation in a PEM reactor. These undesired components existed in higher concentrations after a comparable conventional high-temperature chemical hydrogenation with a Ni catalyst (see Figure 7.18a). Furthermore, it was found that the utilization of gaseous hydrogen clearly decreased the power consumption compared to the operation including water electrolysis, as seen in Figure 7.18b. Fuel Cell Operating Mode The contributions of the research group of Otsuka has been considerable in the ﬁeld of proton-conducting membrane reactors, see for example, (Otsuka, Yamanaka, and Hosokawa, 1990; Otsuka and Yamanaka, 1990, 2000; Yamanaka and Otsuka, 1991; Otsuka, Hashimoto, and Yamanaka, 2002). In their ﬁrst study in 1988, Otsuka et al. used a Pt-bounded Naﬁon 117 membrane as electrolyte at room temperature in a PEM-type membrane reactor. The studied reaction was the partial oxidation of methanol in the gas phase (Yamanaka and

7.4 Membrane Reactors Applying Ion-Conducting Materials 0 Otsuka, 1988). Under open circuit conditions (E cell ) the main product was CO2 (>95% selectivity). In the electrochemical operation the valuable intermediates methyl formate and methylal were formed as main products, and only traces of CO2 were observed. However, due to high internal cell resistances, the attained electric current and accordingly the rate of oxygenate formation remained low. The low productivity due to the low conductivity of solid polymer electrolyte membranes in the preliminary study gave the researchers the impulse for developing a new ion-conducting membrane from phosphoric acid-impregnated silica wool. They reported the successful oxidation of both alkanes (Yamanaka, Hasegawa, and Otsuka, 2002) and methanol in this system (Otsuka, Ina, and Yamanaka, 2003). The conﬁguration allowed them to increase the temperature, which resulted in increased conductivity. The partial oxidation of methanol was studied at temperatures of 70–100 °C with a cell conﬁguration of CH3OH|noble metal|H3PO4 on silica wool|Pt|O2. The operation was carried out under short circuit conditions without a resistance in the external circuit. The cell performance was strongly deteriorated by the crossover of methanol from the anode to the cathode. One successful co-generation of energy and valuable products was published by Yuan et al. (2001). The selective hydrogenation of nitrobenzene to cyclohexylamine was carried out in fuel cell mode, simultaneously producing electric power. The anode and cathode were prepared by hot pressing a carbon-supported Pt-catalyst on a Naﬁon 117 membrane. The measurements were carried out in batch recycle mode for nitrobenzene, obtaining an open circuit voltage of 0.32 V at 70 °C. Negligible amounts of undesired over-oxidation products, cyclohexylamine and aniline, were observed. In fuel cell operation the maximum power density was 1.5 mW cm−2 obtained at a current density of 15 mA cm−2. A reaction time of 2 h gave 8.2% conversion of nitrobenzene, the selectivities being 57.3% and 28.2% to cyclohexylamine and aniline. Another example of fuel cell operation in a chemical reactor from the same group is the hydrogenation of allyl alcohol to 1-propanol accompanied by the cogeneration of electrical energy (Yuan et al., 2003). The selected hydrogenation reaction might not be reasonable in the economic sense, but it can be seen as an interesting model reaction for co-generation in a PEM reactor. The open circuit potential was experimentally determined to be between E0cell = 0.23 to 0.27 V although the standard open circuit potential was calculated to be 0.477 V. The maximum power density was 6.2 mW cm−2 at a current density of 66 mA cm−2. Rather low conversions of allyl alcohol were reported (2.22% in 6 h), but the selectivity to 1-propanol was very high. One special application of membrane reactors working in a fuel cell mode was reported by Sundmacher and Hoffmann (1999). The electrochemical chlorine separation from a nitrogen stream was carried out in a PEM reactor. The reactor operated as a H2/Cl2 fuel cell having an open circuit voltage of 1.36 V. A thin polymer electrolyte membrane layer was applied as a barrier layer between the anode and the liquid electrolyte (HCl) to prevent the break-through of H2 bubbles into the liquid electrolyte layer. High mass transfer rates and current efﬁciencies were obtained when withdrawing the product HCl continuously from the electrolyte layer.

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7 Solid Electrolyte Membrane Reactors

7.5 Conclusions

Solid ion conductors can be used as gas-dense membranes in various technical applications. The most important ﬁelds are electrochemical gas sensors, fuel cells, electrolyzers and solid electrolyte reactors in which ions are transferred through the membrane by an electric ﬁeld applied between the two electrodes. Solid electrolytes (SE) are distinguished by a very high selectivity with respect to the mass transport of the ionic species. Concerning permeability, these materials have to compete with porous membranes and with mixed ion electron conductors (MIEC). With respect to high-temperature oxygen ion conductors, solid oxide fuel cells (SOFC) are still the most important ﬁeld of research and application. However, nowadays new applications are investigated intensively, such as the partial oxidation of light hydrocarbons to oxygenates. High-temperature proton-conducting membranes offer new possibilities for designing solid electrolyte reactors. Therefore, there is need for research on stable protonic electrolytes having high conductivity and active electrodes working in atmospheres with a low level of humidity, both in hydrogen (anodes) and in air (cathodes). Low-temperature proton conductors (PEM) are well established membrane materials in hydrogen fuel cells (PEMFC) and in direct methanol fuel cells (DMFC). In this area, material optimization has to focus on the reduction of the undesired membrane cross-over ﬂuxes of water and methanol. Composite membranes will play an important role for future generations of fuel cells. Moreover, new interesting applications have been reported where PEM reactors are used to carry out selective hydrogenation or selective oxidation reactions in mild conditions. In the future, PEMs might be also good candidates for the realization of microbial fuel cells (see, e.g., Kim et al., 2002) based on mediator-less direct electron transfer. This will require intense collaboration between biochemists and electrochemical engineers.

Acknowledgement

The authors gratefully acknowledge the signiﬁcant contribution of Prof. Helmut Rau during the research project.

Special Notation not Mentioned in Chapter 2 Latin Notation

As Az

m2 m2

CDL CSE

As V−1 m−2 A V−1 m−1

geometrical surface area of Anode cross-sectional area of anode gas channel (reactor shell side) anodic and cathodic double layer capacity SE conductivity constant

Special Notation not Mentioned in Chapter 2

dAC dSE E AA C

m m J mol−1

E Aj E ASE

J mol−1 J mol−1

F FA icell Icell Icell,ref ji

mol s−1 A m−2 A A mol m−2 s−1

kj k 0j k0A C

mol kg−1 s−1 mol kg−1 s−1 mol m−2 s−1

q2/3 relA C

mol m−2 s−1

rel,ref rj RA/C xox,xred

mol m−2 s−1 mol kg−1 s−1 Ω

thickness of anodic catalyst layer SE membrane thickness activation energy for anodic/cathodic charge transfer reaction activation energy for reaction j activation energy for O2− conduction within the SE membrane Faraday constant, (96 485 As mol−1) total molar ﬂow rate within the anode gas channel cell current density total cell current reference cell current molar ﬂow density of species i across the SE membrane reaction rate constant pre-exponential reaction rate constant for reaction j pre-exponential reaction rate constant for anodic/ cathodic charge transfer reaction moles of oxygen required to oxidize 1 mol of n-butane/MA to COx electrochemical charge transfer reaction rate at anode/cathode reference charge transfer reaction rate, (Icell,ref/ASF) reaction rate of reaction j ohmic resistance of anodic/cathodic current collector mole fraction of oxidized/reduced catalyst, (xox + xred = 1)

Greek Notation

α A/C βj ΔΦA/C ΔΦCA ΔΦSE ηA/C νij σ SE

V V V V A V−1 m−1

anodic/cathodic charge transfer coefﬁcient kinetic order of the oxygen species in reaction j anodic/cathodic potential difference local cell voltage, (ΦC–ΦA) potential difference across the SE membrane anodic/cathodic overvoltage stoichiometric coefﬁcients of species i in reaction j conductivity of SE membrane for O2− ions

Characteristic Dimensionless Numbers

Da DaII Φ

Damköhler number, (mcat · rref/FA,0) second kind of Damköhler number Thiele modulus

229

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7 Solid Electrolyte Membrane Reactors

Superscripts

A/C SE

anodic/cathodic solid electrolyte

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Karagiannakis, G., Zisekas, S., and Stoukides, M. (2003) Hydrogenation of carbon dioxide on copper in a H+ conducting membrane-reactor. Solid State Ionics, 162–163, 313–318. Karagiannakis, G., Kokkoﬁtis, C., and Zisekas, S. (2005) Catalytic and electrocatalytic production of H-2 from propane, decomposition over Pt and Pd in a proton-conducting membrane-reactor. Catal. Today, 104, 219–224. Kim, H., Park, H., Hyun, M., Chang, I., Kim, M., and Kim, B. (2002) A mediatorless microbial fuel cell using a metal reducing bacterium, Shewanella putrefaciens. Enzyme Microb. Technol., 30, 145–152. Klose, F., Joshi, M., Hamel, C., and Seidel-Morgenstern, A. (2004) Selective oxidation of ethane over a VOx/γ-Al2O3 catalyst – investigation of the reaction network. Appl. Cat. A Gen., 260, 101– 110. Kobayashi, T., Abe, K., Ukyo, Y., and Iwahara, H. (2002) Performance of electrolysis cells with proton and oxide-ion conducting electrolyte for reducing nitrogen oxide. Solid State Ionics, 154–155, 699–705. Kokkoﬁtis, C., Ouzounidou, M., Skodra, A., and Stoukides, M. (2007) High temperature proton conductors: applications in catalytic processes. Solid State Ionics, 178, 507–513. Kreuer, K.D. (2003) Proton-conducting oxides. Annu. Rev. Mater. Res., 33, 333–359. Krewer, U., Christov, M., Vidakovic, T., and Sundmacher, K. (2006) Impedance spectroscopic analysis of the electrochemical methanol oxidation kinetics. J. Electroanal. Chem., 589, 148–159. Larminie, R., and Dicks, A. (2003) Fuel Cell Systems Explained, John Wiley & Sons, Ltd, Chichester, p. 141. Li, Q., He, R., Jensen, J., and Bjerrum, N. (2004) PBI-based polymer membranes for high temperature fuel cells – preparation, characterisation, and fuel cell demonstration. Fuel Cells, 4, 147–159. Lorences, M.J., Patience, G.S., Diez, F.V., and Coca, J. (2003) Butane oxidation to maleic anhydride: kinetic modeling and byproducts. Ind. Eng. Chem. Res., 42, 6730–6742.

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7 Solid Electrolyte Membrane Reactors Marnellos, G., and Stoukides, M. (2004) Catalytic studies in electrochemical membrane reactors. Solid State Ionics. 175, 597–603. Matsumoto, H., Hamajima, S., Yajima, T., and Iwahara, H. (2001) Electrochemical hydrogen pump using SrCeO3-based proton conductor: effect of water vapor at the cathode on the pumping capacity. J. Electrochem. Soc., 148, D121–D124. Moon, D., and Ryu, J. (2003) Electrocatalytic reforming of carbon dioxide by methane in SOFC system. Catal. Today, 87, 255–264. Munder, B., Ye, Y., Rihko-Struckmann, L., and Sundmacher, K. (2005) Solid electrolyte membrane reactor for controlled partial oxidation of hydrocarbons: model and experimental validation. Catal. Today, 104, 138–148. Munder, B., Rihko-Struckmann, L., and Sundmacher, K. (2007) Steady-state and forced-periodic operation of solid electrolyte membrane reactors for selective oxidation of n-butane to maleic anhydride. Chem. Eng. Sci., 62, 5663–5668. Otsuka, K., and Yamanaka, I. (1990) One step synthesis of hydrogen peroxide through fuel cell reaction. Electrochim. Acta, 35, 319–322. Otsuka, K., and Yamanaka, I. (2000) Oxygenation of alkanes and aromatics by reductively activated oxygen during H2–O2 cell reactions. Catal. Today, 57, 71–86. Otsuka, K., Yamanaka, I., and Hosokawa, K. (1990) A fuel- cell for the partial oxidation of cyclohexane and aromatics at ambient temperatures. Nature, 345, 697–698. Otsuka, K., Hashimoto, T., and Yamanaka, I. (2002) Direct synthesis of hydrogen peroxide (>1 wt%) over the cathode prepared from active carbon and vapor-grown-carbon-ﬁber by a new H2–O2 fuel cell system. Chem. Lett., 8, 852–853. Otsuka, K., Ina, T., and Yamanaka, I. (2003) The partial oxidation of methanol using a fuel cell reactor. Appl. Catal., 247, 219–229. Pfafferodt, M., Heidebrecht, P., Stelter, M., and Sundmacher, K. (2005) Model-based prediction of suitable operating range of a SOFC for an Auxiliary Power Unit. J. Power Sources, 149, 53–62.

Pintauro, P., Gil, M., Warner, K., List, G., and Neff, W. (2005) Electrochemical hydrogenation of soybean oil with hydrogen gas. Ind. Eng. Chem. Res., 44, 6188–6194. Rihko-Struckmann, L., Ye, Y., Chalakov, L., Suchorski, Y., Weiss, H., and Sundmacher, K. (2006) Bulk and surface properties of a VPO catalyst used in an electrochemical membrane reactor: conductivity-, XRD-, TPO- and XPS-study. Catal. Lett., 109, 89–96. Roziere, J., and Jones, D.J. (2003) Nonﬂuorinated polymer materials for proton exchange membrane fuel cells. Annu. Rev. Mater. Res., 33, 503–555. Savadogo, O. (2004) Emerging membranes for electrochemical systems: part II. High temperature composite membranes for polymer electrolyte fuel cell (PEFC) applications. J. Power Sources, 127, 135–161. Schultz, T., Zhou, S., and Sundmacher, K. (2001) Current status of and recent developments in the direct methanol fuel cell. Chem. Eng. Technol., 24, 1223–1233. Schultz, T., Krewer, U., Vidakovic, T., Pfafferodt, M., Christov, M., and Sundmacher, K. (2007) Systematic analysis of the direct methanol fuel cell. J. Appl. Electrochem., 37, 111–119. Simond, O., and Comninellis, C. (1997) Anodic oxidation of organics on Ti/IrO2 anodes using Naﬁon® as electrolyte. Electrochem. Acta, 42, 2013–2018. Spiegel, C. (2007) Designing and Building Fuel Cells, MacGraw-Hill Professional. Srinivasan, S. (2006) Fuel Cells. From Fundamentals to Applications, Springer, Berlin. Staxera (2009) Willkommen bei Staxera, www.staxera.de (accessed 20 April 2009). Stoukides, M. (2000) Solid- electrolyte membrane reactors: current experience and future outlook. Catal. Rev. Sci. Eng., 42, 1–70. Sundmacher, K., and Hoffmann, U. (1999) Design and operation of a membrane reactor for electrochemical gas puriﬁcation. Chem. Eng. Sci., 54, 2937–2945. Sundmacher, K., Schultz, T., Zhou, S., Scott, K., Ginkel, M., and Gilles, E. (2001) Dynamics of the direct methanol fuel cell

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8 Nonlinear Dynamics of Membrane Reactors Michael Mangold, Fan Zhang, Malte Kaspereit, and Achim Kienle

8.1 Introduction

This chapter studies the nonlinear dynamic behavior of membrane reactors. Chapter 1 discusses typical types of membrane reactors. The following focuses on tubular membrane ﬁxed-bed reactors with a nonreactive membrane and chemical reactions on the membrane’s tubular side, as shown in Figure 8.1. The membrane is either used for the separation of products (see Figure 8.1a) or for the distributed injection of reactants (see Figure 8.1b). The objective is to obtain a qualitative understanding of the nonlinear effects in membrane reactors rather than detailed quantitative results. Therefore the analysis is mainly based on simple reactor models. The chapter is divided in two major parts. The ﬁrst part considers the limiting case of inﬁnitely fast reaction rates. This permits comparisons with other reactive and nonreactive separation processes and thus puts membrane reactors in a more general framework. Different wave phenomena are studied. One of the results of this section is the formation of discontinuous spatial temperature and concentration patterns. The second part of the chapter studies this pattern formation in more detail and abandons the assumption of reaction equilibrium.

8.2 Limit of Chemical Equilibrium 8.2.1 Reference Model

Chapter 2 contains a detailed discussion on how to derive membrane reactor models from ﬁrst principles. As this chapter aims at a mainly qualitative understanding of membrane reactor dynamics, simpliﬁed models are considered as most appropriate for the following analysis. In order to obtain such a model for a membrane reactor as illustrated in Figure 8.1, it is assumed that the sweep gas ﬂow is very high, so that all material transported across the membrane is readily Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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Figure 8.1 Operating principle of membrane reactors: a) selective withdrawal of products, b) distributed injection of reactants.

removed and thus the composition in the sweep gas channel does not change. Furthermore, the following assumptions are made:

• • • • • •

The axial dispersion of heat and mass is negligible. The total gas concentration is independent of the composition (ideal mixture). The total pressure is constant. All reactions are equimolar. The ﬂuid and catalyst phases have the same temperature and hence can be modeled by a pseudo-homogeneous energy balance. All components in the mixture have the same heat capacity.

The assumption of equimolar reactions greatly simpliﬁes the mathematics and therefore helps to focus more on the physical interpretation of the results. Under the met assumptions the material balances read in dimensionless form: ∂y ∂y +v = ν r − j + Yj (8.1) tot ∂t ∂z with:

Y , j ∈ RNC −1, r ∈ RNR , ν ∈ R(NC −1) ×NR .

Here, t and z are dimensionless time and space coordinates as deﬁned by (Grüner, Mangold, and Kienle, 2006). NC is the number ofcomponents in the mixture and NRis the number of independent reaction rates. y is the vector of mole fractions, j r is a vector of reaction rates and denotes the ﬂuxes across the membrane. It is worth noting that there are only NC − 1 species but NC independent ﬂuxes, that is, one can either specify NC component ﬂuxes ji or NC − 1 component ﬂuxes and the

8.2 Limit of Chemical Equilibrium

total ﬂow rate jtot. In the remainder, the ﬁrst approach is used, that is, an extended ﬂux vector is deﬁned as: ⎛ j ⎞ (8.2) jext = ⎜ ⎟ ⎝ jtot ⎠ From an energy balance, the following equation for a dimensionless reactor temperature ϑ:= (T − T0)/T0 is obtained: ∂ϑ ∂ϑ T + vε = B r − jϑ ∂t ∂z

(8.3)

The parameter ε stands for the ratio between thermal capacity of the ﬂuid and the total thermal capacity of the system; ε − 1 holds for an empty tubular reactor, ε < 1 for a ﬁxed-bed reactor. B is a vector containing the scaled heat of reaction for each component. The ﬂux jϑ describes the internal energy transported across the membrane, which is a combination of the enthalpy transported by the mass ﬂux and of a heat ﬂux jQ caused by convection. jϑ can be written as: jϑ = ε ∑ ji (ϑ − ϑ i* ) + jQ

(8.4)

where ϑ i* is the temperature of the sweep gas side for ji < 0; ϑ i* = ϑ for ji > 0. From the total material balance and the thermal equation of state, the following differential equation results for the ﬂow velocity:

(

)

∂v ∂ϑ ∂ϑ − jtot = −Cϑ +v ∂z ∂t ∂z

(8.5)

Cϑ is the scaled partial derivative of the total concentration with respect to the temperature; for an ideal gas Cϑ = −1/(1 + ϑ) holds. The following focuses on inﬁnitely fast chemical reactions. The reaction equilibria are given by NR relations: ϑ) = 0 K (y, (8.6) 8.2.2 Isothermal Operation

In a ﬁrst step, the case of isothermal operation is considered. This assumption simpliﬁes the model to: ∂y ∂y +v = ν r (y ) − j (y ) + y j tot (8.7) ∂z ∂t ∂v = − jtot ∂z

(8.8)

8.2.2.1 Nonreactive Membrane Separation In the nonreactive case the reaction rate r is equal to zero and the model equations read:

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Figure 8.2 Nonreactive membrane separation. Parameters: βA = 2.0, βB = 0.2. a) Flux rate ratio of A through membrane versus y~A. b) Response to an input ramp of

∂y ∂y +v = − j (y ) + y j tot ∂t ∂z ∂v = − jtot ∂z

y~A,in, as shown in Figure 8.3. Thin lines = transient solutions at t = 0.2, 0.4, …, 1.2; bold lines = steady state solution.

(8.9) (8.10)

Due to the ﬁnite mass transport kinetics across the membrane this is, even in the nonreactive case, a system of nonhomogenous quasilinear partial differential equations whose properties crucially depend on the ﬂux function j (y ). For simplicity, we focus on a simple diagonal ﬂux function according to: ji = βi yi, i = 1, … , NC.

(8.11)

A discussion of more complicated cases was given for example by Krishna and Wesselingh (1997). Let us illustrate the behavior of the nonreactive membrane separation system with a simple example. Consider a binary mixture with components A, B. Let us assume that the membrane has highest permeability for component A and let us ﬁrst focus on the steady state behavior of such a process. Let Equation 8.9 be the material balance of component A. According to Equation 8.9 the slope of the steady state proﬁle depends on the relative ﬂux ratio jA/jtot and its dependence on the mole fraction y~A. When jA/jtot is larger than y~A then the concentration is decreasing and vice versa. Hence, the qualitative behavior is easily extracted from a diagram of the ﬂux ratio jA/jtot versus concentration y~A, as illustrated on the left side of Figure 8.2. This diagram is the analogon to the well known McCabe–Thiele diagram for distillation processes and nicely illustrates the inﬂuence of mass transfer resistance (Fullarton and Schlünder, 1986). For the simple relation in Equation 8.11 we ﬁnd:

8.2 Limit of Chemical Equilibrium

Figure 8.3 Amp-shaped input of concentration y~A,in used for the startup scenarios in Figures 8.2, 8.4, 8.6.

ji = jtot

βi yi NC

∑ β y

, i = 1, … , N C − 1,

(8.12)

k k

k =1

which is equivalent to the vapor–liquid equilibrium for mixtures with constant relative volatilities. Since the membrane has highest permeability for component A the ﬂux ratio jA/jtot is always larger than y~A. Therefore, the concentration of A is monotonically decreasing in the inner membrane tube and tends to zero for an inﬁnitely long tube. In a similar way the ﬂow rate in the inner tube decreases monotonically and tends to zero. For a tube of ﬁnite length a ﬁnite ﬂow rate and a ﬁnite concentration is obtained. The dynamic transient behavior during start-up is illustrated on the right side of Figure 8.2. Figure 8.3 shows the ramp-shaped inlet concentration belonging to this start-up scenario. Like in reactive distillation and reactive chromatography (Grüner, Mangold, and Kienle, 2006), the transient behavior is governed by traveling fronts. In the present case, these waves can only propagate downstream. Further, since the velocity in the inner tube is decreasing continuously from the inlet to the outlet due to material transport across the membrane, concentration values closer to the inlet move with higher velocity than concentration values closer to the outlet. Consequently, all waves are self-sharpening in Figure 8.2. Alternatively, also inlet concentration disturbances of the steady-state proﬁle may be considered. Due to the inhomogeneity in Equation 8.9 the concentration waves travel downstream on the nonconstant initial proﬁle as the system undergoes a transient from the old to a new monotonically decreasing steady state. The same type of dynamics can be observed in the multicomponent case. Any step disturbance is resolved into a single front traveling jointly for all components, due to the fact that all balance equations share the same transport velocity v. This

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simple behavior is in contrast to the more complex wave phenomena found in distillation and chromatographic processes (Grüner, Mangold, and Kienle, 2006; Kienle, 2000). 8.2.2.2 Membrane Reactor In the reactive case, the full blown Equation 8.7 together with the total material balance (8.8) has to be considered. For fast chemical reactions, reaction equilibrium can be assumed. The chemical equilibrium conditions represent NR algebraic constraints, which reduce the dynamic degrees of freedom of the system to NC − 1 − NR. In the limit of reaction equilibrium, the kinetic rate expressions for the reaction rates become indeterminate and have to be eliminated from the balance equations (8.7). Following the ideas of (Ung and Doherty, 1995), this is achieved by choosing NR reference components and splitting the concentration vector accordingly into two parts: (8.13) y = ⎡⎣y I , y II ⎤⎦ , y I ∈ RNR , y II ∈ RNC −1−NR

An analogous splitting is introduced for the matrix of stoichiometric coefﬁcients:

ν = ⎡ν , ν ⎤ , ⎣⎢ ⎦⎥ I

II

(8.14) II

I

where ν has dimensions NR × NR and ν has dimensions (NC − 1 − NR) × NR. By solving the ﬁrst NR equations of (8.7) for the unknown reaction rates and substituting them into the remaining NC − 1 − NR equations, the following reduced set of equations is obtained: ∂Y ∂Y (8.15) +v = − J (y ) + Y J tot. ∂t ∂z ∂v = − J tot ∂z

(8.16)

with transformed concentration and ﬂux variables according to:

()

II I Y = y II − ν ν

−1

()

II I y I, J = j II − ν ν

−1

()

II I II j I, J ext = jext − ν ext ν

Y ∈ RNC −1−NR , J ∈ RNC −1−NR , J ext ∈ RNC −NR

−1

j I

(8.17)

It is worth noting that, like in the nonreactive case, the dimension of the ﬂux vector J ext exceeds the dimension of the concentration vector by one. Conse II quently, the dimension of jext exceeds the dimension of y II by one and the matrix II II ν ext consists of matrix ν with an additional row for component NC. In the above equations the relation Jtot = jtot is used. This follows from the deﬁnition of Jtot: J tot =

NC − N R

∑ i =1

Ji =

NC − N R

∑ i =1

()

NR II I ⎛ j − ν ext ,i ν i ∑ ⎜⎝ j =1

−1 j

⎞ jj⎟ ⎠

(8.18)

8.2 Limit of Chemical Equilibrium

and the constant total mole number for each reaction according to: NC − N R

∑ i =1

NR

II

I

ν ext ,i = − ∑ ν i,

(8.19)

i =1

II

I

respectively. In the above equations ν ext ,i, ν i represent the i-th row vector of the corresponding matrix and

() ν

I −1

represents the j-th column vector of the j

corresponding inverse matrix. Hence: NC − N R

∑ i =1

NR

II

()

ji − ∑ ν ext ,i ν j =1

I −1 j

jj =

NC − N R

∑ i =1

NR

NC

i =1

i =1

ji + ∑ ji = ∑ ji = jtot

(8.20)

The reactive problem in transformed concentration variables (8.15), (8.16) is completely analogous to the corresponding nonreactive problem (8.9), (8.10) and we can proceed in a similar way like in the previous section to investigate the qualitative behavior. The same analogies can be drawn for reactive distillation and reactive chromatography, as discussed by (Grüner, Mangold, and Kienle, 2006). In a ﬁrst step we focus on a single reversible reaction of type 2A ↔ B + C. The treatment for the corresponding problems in reactive distillation and reactive chromatography was given by (Grüner and Kienle, 2004). In particular, it was shown that total conversion in an inﬁnitely long column is only possible if reactant A has intermediate afﬁnity to the vapor or the solid phase, respectively. In the other cases, achievable product compositions are limited by reactive azeotropy. Conditions for total conversion in a membrane reactor, however, are more restrictive. In the present case the total conversion of reactant A is only possible if the membrane is not permeable at all for reactant A and at least one of the products is continuously removed to shift the equilibrium to the product side. If, in addition, the membrane has zero permeability for the other product, simultaneous separation of the products is achieved. This situation is illustrated in Figure 8.4 with the transformed concentration and ﬂux variables as introduced in Equation 8.17. Therein, component A is taken as the reference, which leads to the following deﬁnitions: y A YB = yB + , YC = 1 − YB, (8.21) 2 jA jA JB = jB + , J C = jC + , 2 2 (8.22) J tot = JB + JC = jA + jB + jC = jtot. Further, it is assumed in Figure 8.4 that the membrane is only permeable for product B but not for product C. For the simple system considered here, the ﬂux rate ratio shown in Figure 8.4 can be calculated explicitly. It is equivalent to a reactive vapor–liquid equilibrium with zero volatility for reactant A due to zero permeability of the membrane for this component. In the transformed concentration variables a YB value of zero corresponds to pure product C, a value of 0.5 to pure reactant A and a value of 1.0 to pure product B. It should be noted that the diagram on the left of Figure 8.4 has the same structural properties as the corresponding diagram of Figure 8.2 for

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Figure 8.4 Membrane reactor with a reaction 2A ↔ B + C. Parameters: βA = βC = 0, βB = 1, K = 1. a) Transformed ﬂux ratio versus YB. b) Response to input

ramp of YB,in or y~A,in, respectively, as shown in Figure 8.3. Thin lines = transient solutions at t = 0.3, 0.6, …, 3.3; bold lines = steady state solution.

the nonreactive binary case. In particular, the steady-state proﬁle of YB in the inner tube will monotonically decrease and tend to YB = 0, which corresponds to pure product C in the inner tube. The dynamic transient behavior during start-up is also analogous to the nonreactive case considered in Figure 8.2. In practice, the membrane however often has ﬁnite permeability for all components, which is considered next. In this case the enhancement of the reaction through the membrane strongly depends on the order of permeability of the membrane for the different components. In particular, three different cases are considered, where the membrane has highest, intermediate or lowest permeability for reactant A. The permeability for B is assumed to be higher than for C in all three cases. Like in the previous case an explicit calculation of the transformed ﬂux rate ratio is possible. The results are shown in Figure 8.5. These diagrams are exactly the same as the McCabe–Thiele diagrams for the corresponding ternary reactive distillation processes (Grüner and Kienle, 2004), which are equivalent to McCabe–Thiele diagrams for binary nonreactive mixtures. The case with intermediate permeability corresponds to the nonreactive vapor liquid equilibrium of an ideal binary mixture, whereas the other two cases correspond to the nonreactive vapor liquid equilibrium of azeotropic binary mixtures. According to the terminology introduced by (Huang et al., 2004), these ‘azeotropic points’ are called reactive arheotropes in the remainder. At these points the change of concentration through reaction and through mass transport across the membrane compensate each other and lead to constant composition. The corresponding proﬁles of the transformed concentration variables and the velocity v are shown in Figure 8.5. In the ﬁrst case, the reactive arheotrope represents the maximum achievable composition which can be obtained in the inner tube of an inﬁnitely

Figure 8.5 βC = 1.

Membrane reactor with a reaction 2A ↔ B + C. Parameters: K = 1, a) βA = 1, βB = 5, βC = 3, b) βA = 3, βB = 5, βC = 1, c) βA = 5, βB = 3,

8.2 Limit of Chemical Equilibrium 243

244

8 Nonlinear Dynamics of Membrane Reactors

Figure 8.6 Membrane reactor with a reaction 2A ↔ B + C, response to input ramp of YB,in or y~A,in, respectively, as shown in Figure 8.3.Thin lines = transient solutions at t = 0.2, 0.4, …, 1.2, bold lines = steady state

solution. a) βA = 1, βB = 5, βC = 3, b) βA = 3, βB = 5, βC = 1, c) βA = 5, βB = 3, βC = 1. Dotted lines in a) mark composition at the arheotropic point.

long membrane reactor when the feed is pure reactant A. In the other two cases pure product C can be obtained in the inner tube. However, total conversion is of course not possible due to the loss of reactant across the membrane, due to the ﬁnite permeability for A. Again the qualitative dynamic behavior, which is illustrated in Figure 8.6 for a start-up scenario, is completely analogous to the nonreactive case. In particular, in the ﬁrst case the self-sharpening characteristic of the traveling concentration fronts is very pronounced. Again, this comes from the decrease of the transport velocity from the entrance to the outlet. An extension to multireaction and multicomponent systems with more than one independent variable is straight forward. Feasible products follow from the corresponding reactive residue curve maps for membrane processes, as introduced by (Huang et al., 2004). Propagation dynamics follow from the variable transport velocity v, which is the same for all components. Step disturbances therefore also in the reactive case be resolved into a single wave traveling jointly for all (transformed) concentrations. The variable velocity v results in self-sharpening waves.

8.2 Limit of Chemical Equilibrium

8.2.3 Nonisothermal Operation 8.2.3.1 Formation of Traveling Waves First the case of an empty tubular reactor with ε = 1 is considered. In analogy to the isothermal case, the following reduced set of equations is obtained from (8.1) and (8.3) by a state transformation: ∂ ⎛Y ⎞ ∂ ⎛Y ⎞ ⎛ J ⎞ ⎛Y ⎞ + v = − + (8.23) ⎜⎝ ⎟⎠ ⎜⎝ ⎟⎠ J tot ∂t ⎜⎝ Θ⎟⎠ ∂z ⎜⎝ Θ⎟⎠ JΘ 0 The deﬁnition of Y , J,Jtot is identical to the isothermal case (8.17). The temperature and heat ﬂuxes are transformed according to: I −1 I −1 Θ = ϑ − BT ν y I, JΘ = jϑ − BT ν ( j I − y I jtot ) (8.24)

()

()

To obtain the total material balance (8.5) in transformed coordinates, the ∂ϑ ∂ϑ has to be computed from the transformation relation: expression +v ∂t ∂z −1 ∂y I ⎞ ⎛ ∂Y ⎛ II I ⎞ ⎛ ∂y I ∂Y ⎞ − ν ν I 0 v + +v ⎜ ⎟ ⎜ ∂t ∂z ⎟ ⎜ ∂t ∂z ⎟ II ⎟ ⎜ ⎜ ⎟ ⎜ II ⎟ 1 − I ∂y ⎟ ⎜ ∂ Θ ∂Θ ⎟ ⎜ ⎟ ⎜ ∂y (8.25) v + B ν 0 1 v = + ⎟ ⎜ ∂t ⎜ ∂z ⎟ ⎜ ∂ t ∂ z ⎟ ⎟ ⎜ ⎜ ⎟⎜ ⎟ 0 ∂K ∂K ⎟ ⎜ ∂ϑ + v ∂ϑ ⎟ ⎜ ⎜ ∂K ⎟ ⎠ ∂z ⎠⎟ ⎝ ⎝⎜ ∂y I ∂y II ∂ϑ ⎟⎠ ⎝⎜ ∂t

() ()

It is obvious from Equation 8.23 that – as in the isothermal case – in the nonisothermal case concentration and temperature waves also travel with an identical velocity, which is the ﬂow velocity of the ﬂuid. Sharpening or expansion of the waves may occur, if the ﬂow velocity changes along the space coordinate. The situation is different for ﬁxed-bed membrane reactors, where ε < 1. In this case, thermal fronts may spread with a velocity different from the ﬂow velocity of the ﬂuid. This is discussed in the following for the special case of a single reaction, where it is easily possible to calculate the velocity of a thermal front explicitly. Using the reaction equilibrium (8.6) and the material balance (8.1) for y~I, the following relation for the reaction rate is obtained: II II ∂y II ⎞ ∂K ∂ϑ ∂ϑ ∂ϑ ⎫ I −1 ⎧ ∂K ∂y ⎛ ∂y I I r = (ν ) ⎨ − +v ⎟⎠ − ∂K ∂y I ∂t + v ∂z + j − x jtot ⎬ (8.26) I ⎜ ⎝ ∂ K ∂ y ∂ t ∂ z ⎩ ⎭ II Inserting this into the material balances for y as well as into the energy balance (8.3) yields: ∂y II ⎞ ⎛ ∂y II 0 ⎛ ⎞ ⎛ II I I I + v ⎜ ν ν ( j − y jtot ) − j II + y II jtot ⎞ ∂z ⎟ = ⎜ ⎟ M ⎜ ∂t + ⎟ ∂ϑ ⎜ ⎟ (8.27) ⎠ B ν I ( j I − x I jtot ) − jϑ ⎜ ∂ϑ + v ∂ϑ ⎟ ⎜⎝ − (ε − 1) v ∂z ⎟⎠ ⎝ ⎝ ∂t ∂z ⎠

(

)

245

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8 Nonlinear Dynamics of Membrane Reactors

The left-hand side matrix M reads: II II ⎛ I ⎞ ⎛ ∂K ∂y ∂K ∂ϑ ⎞ M = I − ⎜ν ν ⎟ ⎜ , K ∂y I ∂K ∂y I ⎟⎠ ⎝ B ν I ⎠ ⎝∂ T

(8.28)

= :q

=:l

If M is regular, the above equations can be decoupled by inversion of M. When doing this, one ﬁnds for the propagation velocity of a temperature front vϑ: vϑ = ε v − (1 − ε ) v

B ν I ⋅ ( ∂K ∂ϑ ) ( ∂K ∂y I ) 1 − l Tq

(8.29)

Depending on the properties of the reaction equilibrium, expanding temperature waves, sharpening waves and discontinuous shocks can evolve. Shock solutions of this type were analyzed by (Glöckler, Kolios, and Eigenberger, 2003) for a reverse-ﬂow ﬁxed-bed reactor. 8.2.3.2 Formation of Discontinuous Patterns Nonisothermal operation can lead to another interesting phenomenon when the membrane is used not for the separation but for the injection of reactants (Figure 8.1b). In this case, concentration and temperature patterns may form. This effect is studied in detail in the next section. Here, some preliminary considerations are made, again assuming that the reaction rate is inﬁnitely fast. It is shown that spatiotemporal patterns can also occur in the limiting case of reaction equilibrium and that those patterns may contain discontinuities. As an example, the reversible reaction A ↔ B is considered. Additional model assumptions are:

•

The reaction equilibrium reads: yBeq ⎛ γϑ ⎞ = k eq exp ⎜ , ⎝ 1 + γϑ ⎟⎠ y Aeq

(8.30)

where γ is the dimensionless free enthalpy of reaction.

•

The reaction rate is: r = k0r ′ ( y A, yB, ϑ ) ,

(8.31)

where k0 is a rate constant that tends to inﬁnity in the limiting case, and r′ is some function that vanishes at the reaction equilibrium.

• • • •

The mixture in the reactor consists of the two reactants A and B and an inert I. S The sweep gas side of the reactor contains pure A, that is, y A = 1. The membrane is permeable for all three components, the ﬂow rates given as: ji = βi ( yi − yiS ). The convective heat ﬂux across the membrane is: jQ = α(ϑ − ϑS). The reactor is a tubular reactor with ε = 1.

In the following, we consider the behavior of the system along a characteristic direction ξ, where:

8.2 Limit of Chemical Equilibrium

dz dt = v, = 1. dξ dξ

(8.32)

From the material balances (8.1) and the energy balance (8.3), one obtains the differential equations: dy A = −k0r ′ − jA + y A jtot dξ

(8.33)

dyB = k0r ′ − jB + yB jtot dξ

(8.34)

dϑ = Bk0r ′ + jϑ dξ

(8.35)

By introducing the transformed variables: YA := y A, YB := y A + yB, Θ := By A + ϑ ,

(8.36)

the above system of equations is converted to: 1 dYA 1 = −r ′ + ( − jA + y A jtot ) k0 dξ k0

(8.37)

dYB = − JB + YB J tot dξ

(8.38)

dΘ = − JΘ dξ

(8.39)

The reaction equilibrium, given by r′ = 0 or (8.30), deﬁnes the quasi-stationary manifold of the system (8.37–8.39) for k0 → ∞. In the case of an inﬁnitely fast reaction rate, the solutions of (8.37–8.39) move along that manifold. Discontinuities and relaxation oscillations may occur, if for given values of YB and Θ the value of YA on the quasi-stationary manifold is not unique. An example is shown in Figure 8.7. The trajectory remains on the quasi-stationary manifold until it reaches a minimum point on the manifold. At that point, the solution jumps to a different value of YA. The values of YB and Θ do not change at the discontinuity, that is: YB− = YB+,

(8.40)

Θ − = Θ +,

(8.41)

where “−” indicates the state immediately before the discontinuity, and “+” the state immediately after the discontinuity. In original variables, (8.40) and (8.41) read: y A− − y A+ = yB+ − yB−,

(8.42)

ϑ + − ϑ − = B( y A− − y A+ ) .

(8.43)

That is, (8.40) and (8.41) ensure the conservation of mass and the conservation of energy at the discontinuity. Figure 8.8 shows the relaxation oscillation in original variables.

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8 Nonlinear Dynamics of Membrane Reactors

Figure 8.7 Transient of the nonisothermal membrane reactor model (8.37–8.39) to a relaxation oscillation in transformed variables. The gray mesh indicates the shape of the quasi-stationary manifold; black solid

lines = trajectories on the manifold; black dashed lines = discontinuous parts of the S solution. Parameter values: yA = 1 , ϑS = 0, βA = βI = 1, βB = 10, α = 3, γ = 1000, B = 0.0162, keq = 0.0143.

8.3 Pattern Formation

The formation of spatial patterns in membrane reactors with side injection is studied in more detail in the following. A number of publications show that the side injection of reactants may cause quite complicated nonlinear behavior (Nekhamkina et al., 2000a, 2000b; Sheintuch and Nekhamkina, 2003; Travnickova et al., 2004). Sheintuch and co-workers pointed out an analogy between the dynamic behavior of a CSTR and the steady-state behavior of an ideal plug ﬂow membrane reactor. They showed that for a small axial dispersion of heat spatially periodic patterns can emerge for an exothermic ﬁrst-order reaction (Nekhamkina et al., 2000a) and that complex aperiodic patterns may exist in the case of a simple consecutive reaction with two reaction steps (Sheintuch and Nekhamkina, 2003). (Travnickova et al., 2004) found complex aperiodic spatiotemporal patterns in a cross-ﬂow reactor with a ﬁrst-order reaction and high axial dispersion of heat. In this section, we explore the possibility of obtaining and measuring stationary spatially periodic patterns in a laboratory membrane reactor. Different models of a membrane reactor with a porous membrane and a catalytic ﬁxed bed are considered. All models use an experimentally validated reaction scheme for the partial oxidation of ethane. It should be noted that the partial oxidation reaction serves

8.3 Pattern Formation

Figure 8.8 Discontinuous solutions of the nonisothermal membrane reactor model (8.37–8.39) along a characteristic ξ in original variables; parameter values as in Figure 8.7.

only as an example and similar qualitative behavior may be expected for other exothermic reactions in membrane reactors. The simplest model variant assumes ideal plug ﬂow behavior in the ﬁxed bed. It is studied in the ﬁrst step by a bifurcation analysis and by dynamic simulations. In the second step, dispersive effects are included in the analysis. In the last step, the results are compared with a more detailed spatially distributed model of the membrane reactor. 8.3.1 Analysis of a Simple Membrane Reactor Model

(Klose et al., 2004) investigated the oxidative dehydrogenation of ethane over a VOx/γ-Al2O3 catalyst in a laboratory ﬁxed-bed reactor. As discussed in Chapter 3, kinetic expressions were derived for this reaction. The reaction network proposed by (Klose et al., 2004) consists of ﬁve reaction steps (see Figure 8.9). Reaction 1 is described by a Mars van Krevelen mechanism. For reactions 2–5, a Langmuir– Hinshelwood approach is used. All kinetic equations and parameters are given in Section 3.4. This work investigates the oxidative dehydrogenation of ethane in a ﬁxedbed membrane reactor with side injection of reactants, as shown in Figure 8.1b. The reactor consists of a porous tubular membrane and a catalytic ﬁxed bed

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8 Nonlinear Dynamics of Membrane Reactors

Figure 8.9

Reaction network for the oxidative dehydrogenation of ethane (Klose et al., 2004).

Figure 8.10 Physical interpretation of the stationary pattern formation in a ﬁxed-bed membrane reactor. Meaning of ﬁlled arrows: ↑ = charging of energy storage by chemical reaction; ↓ = discharging of energy storage

by heat losses. Meaning of open arrows: ↑ = charging of mass storage by mass supply through membrane; ↓ = discharging of mass storage by chemical reaction.

inside the tube. The shell side of the membrane is empty. Reactants can be fed directly to the inlet of the ﬁxed bed with concentrations c˜i,in and a temperature Tin; alternatively they can enter the ﬁxed bed in a spatially distributed manner via the shell side across the membrane with inlet concentrations c˜0i and an inlet temperature T0. Figure 8.10 gives a simple physical explanation for the possible formation of spatial patterns in such a reactor. The ﬂuid ﬂowing through the ﬁxed bed possesses a storage capacity for material of reactants and for heat. A spatial pattern is caused by the alternate charging and discharging of the material storage and the heat storage resulting from the chemical reaction. In sections of high

8.3 Pattern Formation

conversion, the material storage is discharged, and the reaction heat released charges the energy storage. In sections of low conversion, the material storage is reloaded by mass transfer from the sweep gas side through the membrane, while heat losses reduce the temperature of the ﬁxed bed and hence discharge the energy storage. In order to verify the pattern formation in the case of ethane oxidation, a onedimensional pseudo-homogeneous model of the membrane reactor is used in this Section. Radial concentration and temperature gradients as well as a change in the axial ﬂow rate due to mass transport through the membrane are neglected. The concentration and temperature on the shell side of the membrane are assumed to be constant and identical to the inlet conditions c˜0i and T0. The reactants are assumed to behave like ideal gases. The differential equations for the concentration and the temperature inside the ﬁxed bed are obtained from mass and energy balances. They account for accumulation, convection, axial dispersion, chemical reactions, heat transfer through the membrane and mass supply through the membrane. The component mass balances read: 5 ∂ci ∂ci 2 = −v + ∑ ν ijr j ρcat + β ( c0i − ci ) , i = 1, … , 5 ∂t ∂z j = 1 R

(8.44)

The energy balance leads to:

( ρc P )tot

5 ∂T ∂T ∂2T 2 = − v ( ρc P )f + λ 2 + ∑ ν ij ( − ΔRH ) j r j ρcat + α (T0 − T ) ∂t ∂z ∂z R j =1

(8.45)

In the model, the heat of reaction varies with temperature; the partial molar enthalpy of each component is computed from: hi = hi ,ref + c P ,i (T − Tref )

(8.46)

for the values of the enthalpies of formation for each component. The following boundary conditions are used for (8.44) and (8.45): ci ( 0, t ) = ci ,in (t ) , i = 1, … , 5, λ ∂T ∂z

=0

∂T ∂z

= v ( ρc P )f [T ( 0, t ) − Tin (t )]

(8.47)

0,t

(8.48)

L ,t

The set of model equations is completed by a quasi-stationary equation of continuity that determines the ﬂow velocity v. ∂ρ f v = 0, v ( 0, t ) = vin (t ) ∂z

(8.49)

The ﬂuid density ρf follows from the ideal gas law. In the above equations, t and z are the time and the space coordinates, v is the ﬂow velocity of the gas, c˜1 – c˜5 stand for the molar concentrations of the components (respectively: ethane, ethene, carbon monoxide, carbon dioxide, oxygen), vij are the stoichiometric coefﬁcients, R is the inner radius of the membrane, β is a mass transfer coefﬁcient, (ρcP)tot and (ρcP)f are, respectively, the thermal capacities of the ﬁxed bed and the

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8 Nonlinear Dynamics of Membrane Reactors

gas, λ is the axial heat conductivity of the bed and α is a heat transfer coefﬁcient. All model parameters used in the simulations are listed by (Zhang, Mangold, and Kienle , 2006). 8.3.1.1 Analysis of Steady-State Reactor Behavior for Vanishing Heat Dispersion The analysis of the membrane reactor behavior becomes comparatively simple when the heat dispersion term in Equation 8.45 is neglected. In this case, the steady-state component mass balances and the steady-state energy balance read:

v

5 ∂ci 2 = ∑ ν ijr j + β ( c0i − ci ) , ci (0 ) = ci ,in, i = 1, … , 5 ∂z j = 1 R

v ( ρc P )f

5 ∂T 2 = ∑ ν ij ( − ΔRH ) j r j + α (T0 − T ) , T (0 ) = Tin ∂z j = 1 R

(8.50)

(8.51)

Obviously, there is an analogy between the above steady-state equations of an ideal plug ﬂow membrane reactor and the dynamic equations of a CSTR (Nekhamkina et al., 2000a). The dynamic behavior of exothermic CSTRs has been studied in detail and found to be surprisingly complex, even for simple ﬁrst-order reactions (Uppal and Ray, 1974; Sheplev, Treskov, and Volokitin, 1998). Therefore, an analogous pattern of behavior can be expected for the steady-state solutions of the plug ﬂow membrane reactor considered here. In a ﬁrst step, spatially homogeneous solutions are investigated, which correspond to the steady-state solutions of a CSTR. The continuation methods in DIVA (Mangold et al., 2000) are used to analyze the dependence of the solutions on the shell side concentrations c˜0i and the shell side temperature T0 as the main operation parameters. An example for the results is given in Figure 8.11. Saddle node bifurcations and Hopf bifurcations are found when the temperature and the concentration on the shell side are varied. The curve of saddle node bifurcations in Figure 8.11a borders a region of multiple spatially homogeneous solutions, that is, inside this region there are three different sets of reactor inlet conditions, resulting in three different spatially homogeneous solutions for given shell side conditions. Figure 8.11 also contains information on the stability of the steady-state solutions of Equations 8.50 and 8.51 when moving along the space coordinate z. Stability means in this case that, as z increases, the composition and temperature in the ﬁxed-bed approach asymptotically the homogeneous solution, that is, the steady-state solution of Equations 8.50 and 8.51, if c˜i,in and Tin are close to but not identical to the homogeneous solution. Obviously, this notion of stability has to be distinguished from the dynamic stability of the homogeneous solutions of Equations 8.44 and 8.45. The curve of Hopf bifurcation points indicates locations in parameter space where spatially periodic solutions emerge. Only simple period 1 solutions are found when just ethane and oxygen are fed through the membrane. However, the behavior becomes more complex when ethene is also added to the feed, as can be seen from Figures 8.12 and 8.13. Figure 8.12 shows a bifurcation diagram obtained by a continuation of spatially periodic solutions. Under the chosen operation conditions, a sequence of period-doubling bifurcations is found. Selected periodic solutions from the period 1, period 2,

8.3 Pattern Formation

Figure 8.11 Analysis of spatially homogeneous solutions of the ideal plug ﬂow membrane reactor. a) Saddle node bifurcations (solid lines) and Hopf bifurcations (dotted lines), when shell side temperature and shell side mole fraction of ethane are used as bifurcation parameters. b) One parameter continuation with the shell side mole fraction of ethane as continuation parameter and a constant shell side temperature T0 = 848 K (along the vertical

dashed line in Figure 8.11a). c) One parameter continuation with the shell side temperature as continuation parameter and a constant shell side mole fraction of ethane y~0,C2H6 = 0.04 (along the horizontal dashed line in Figure 8.11a); solid lines in b) and c) denote stable solutions, dashed lines denote unstable solutions, squares denote Hopf bifurcation points. The asterisk in a) and the arrow in b) indicate the simulation conditions of Figure 8.14.

period 3 and period 4 branches are shown in Figure 8.13a–c. In the vicinity of the period 4 solution branch, even more complex aperiodic solutions are found, as can be seen in Figure 8.13d. The aperiodic solution in Figure 8.13 is examined more closely by calculating the Lyapunov exponents according to the method given by (Wolf et al., 1985; Benettin et al., 1980; Shimada and Nagashima, 1979), assuming that the reactor has an inﬁnite length. The three leading Lyapunov exponents found are: λ1 = 0.1765, λ2 = 0.0 and λ3 = −3.649, respectively. The positive Lyapunov exponent λ1 is an indicator of deterministic chaos. The Lyapunov dimension DL of the aperiodic attractor is calculated according to the Kaplan–Yorke conjecture (Yorke and Kaplan, 1979) from: DL = 2 +

λ1 + λ 2 λ3

(8.52)

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8 Nonlinear Dynamics of Membrane Reactors

Figure 8.12 Continuation of periodic solutions of the ideal plug ﬂow membrane reactor model. Circles indicate period-1 solutions, squares indicate period-2 solutions, triangles indicate period-4 solutions. Filled symbols denote stable

solutions, open symbols denote unstable solutions. Operation conditions on shell side: shell side temperature T0 = 820 K, shell side mole fraction of ethane y~0,C2H6 = 0.02, other conditions as in Figure 8.11.

The resulting value of DL = 2.048 is slightly above the lower limit of 2.0 for chaotic attractors. In conclusion, the ideal plug ﬂow reactor model shows a complex steady-state behavior. Some of the pattern solutions found possess maximum temperatures beyond the validity limit of the model. Nevertheless, those solutions indicate operation conditions where interesting phenomena may also occur in more detailed models. As an example, the inﬂuence of axial dispersion of heat is studied in the next section. 8.3.1.2 Inﬂuence of Heat Dispersion Figure 8.14 shows steady-state temperature proﬁles for various values of the axial heat conductivity λ. The operation conditions used are indicated in the bifurcation diagram, Figure 8.11. The steady-state solutions are computed by applying the method of lines to the model (8.44–8.49) using 4000 ﬁnite volumes. The resulting algebraic equations are solved by the damped Newton method NLEQ1S (Nowak and Weimann, 1990). For small values of λ, the patterns agree with the results of the ideal plug-ﬂow membrane reactor model obtained by integration along the space coordinate using the integrator DDASAC (Caracotsios and Stewart, 1985). This indicates a reasonable accuracy of the discretized model. For large values of λ the axial heat conduction counteracts the pattern formation and smoothes the temperature proﬁle. The patterns vanish completely when λ exceeds a maximum value, which can be determined by linear analysis (Nekhamkina et al., 2000b).

8.3 Pattern Formation

Figure 8.13 Examples of pattern solutions of the ideal plug ﬂow membrane reactor. a) Period-1 oscillation with shell side temperature T0 = 820 K, shell side mole fractions y~0,C2H6 = 0.02, y~0,C2H4 = 0.0313, other conditions as in Figure 8.11 a). b) Period-2

oscillation with y~0,C2H4 = 0.0315, other conditions as in a). c) Period-4 oscillation with y~ = 0.0317, other conditions as in 0,C2H4

a). d) Aperiodic solution with T0 = 820.8 K, y~ = 0.0318, other conditions as in a). 0,C2H4

For values of the heat conductivity below this limit, the pattern solution seems to undergo bifurcations: The period of the pattern doubles suddenly for values of λ between 0.0201 and 0.0202 W m−1 K−1 (see Figure 8.15). The dynamic behavior of the system is shown in Figures 8.16 and 8.17. A spatially homogeneous proﬁle is used as initial condition. At the beginning of the simulation, a pattern with a rather short wavelength forms. This pattern moves in the direction of the gas ﬂow towards the reactor outlet. The remaining stationary pattern possesses a longer wave length and a smaller amplitude. 8.3.2 Detailed Membrane Reactor Model

In order to explore the possibility of ﬁnding stationary patterns in a laboratory membrane reactor, the following considers a more detailed reactor model. This

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8 Nonlinear Dynamics of Membrane Reactors

Figure 8.14 Stationary patterns of an ideal plug ﬂow membrane reactor and a membrane reactor model with axial heat dispersion for λ = 0.1, 0.4 and 1.0 W m−1 K−1 (from top to bottom, respectively). T0 = 848 K, y~0,C2H6 = 0.027, other parameters as in Figure 8.11.

model describes the catalytic ﬁxed bed inside a porous membrane, the heat and mass transport through the membrane and the sweep gas side outside the membrane. The model is implemented in the ProMoT process modeling tool, using a model library for membrane reactors available with this software (Mangold, Ginkel, and Gilles, 2004). 8.3.2.1 Main Model Assumptions The differences between the complete model and simple model are listed below.

•

The ﬁxed bed is described in a model as in Equations 8.44–8.49, with the main difference that the dependence of the heat capacities and the total molar mass on the composition of the gases is taken into account.

•

The temperature and composition on the sweep gas side are no longer assumed to be constant but are calculated from model equations similar to (8.44–8.49) without the reactive term. Heat loss to the outer reactor wall is described by constant heat transfer parameter, assuming a constant wall temperature.

8.3 Pattern Formation

Figure 8.15 Stationary patterns of the temperature for λ = 0.01, 0.0201, 0.0202, 1.0 W m−1 K−1 (from top to bottom, respectively). T0 = 820 K, y~0,C2H6 = 0.02, y~0,C2H4 = 0.319, other parameters as in Figure 8.11.

•

A more detailed model is used to simulate the mass and heat transfer through the membrane. This model is introduced in the following section.

8.3.2.2 Model Equations of the Membrane The model used here to describe mass transport through the membrane is a simpliﬁed version of the model developed by (Hussain, Silalahi, and Tsotsas, 2004). The membrane under consideration consists of four ceramic layers with different porosities. The mass ﬂux through each layer can be described by the dusty gas law (cf. Chapter 2). Neglecting interactions between the components and approximating the partial pressure gradients by the partial pressure differences on both sides of a membrane layer, one obtains for the molar ﬂux of component j through layer i:

n ij = −

1 8 RTmem B0i ⎞ ⎛4 + K 0i P ΔPi , j, i = 1, … , 4, j = 1, … , 7 j RTmemdi ⎜⎝ 3 πM η j ⎟⎠

(8.53)

In the above equation, di is the thickness of layer i and B0i and K0i are the permeabil¯ is the mean ity constant and the Knudsen coefﬁcient of the layer, respectively. P

257

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8 Nonlinear Dynamics of Membrane Reactors

Figure 8.16 Contour plot showing the formation of a sustained pattern starting from a spatially homogeneous initial proﬁle. T0 = 848 K, y~0,C2H6 = 0.025 and λ = 0.01 W m−1 K−1, all other parameters as in Figure 8.11.

pressure in the membrane, which is set to 1 bar (= 100 kPa) in the simulation. Tmem is the temperature in the membrane, which is set to: Tmem =

Tsw + Tfb 2

(8.54)

where TSW is the local temperature on the sweep gas side, and Tfb is the local temperature of the ﬁxed bed. The parameters of the membrane layers are taken from (Hussain, Silalahi, and Tsotsas, 2004). Assuming a negligible hold-up of the membrane, the molar ﬂuxes are coupled by: n j ,1 = n j ,2 = n j ,3 = n j , 4

(8.55)

The following summation conditions hold for the partial pressure differences: 4

∑ ΔP

i, j

= Psw , j − Pfb, j, j = 1, … , 7

(8.56)

i =1

The heat transfer from the sweep gas through the membrane to the ﬁxed bed is described by: q = α mem ⋅ (Tsw − Tfb )

(8.57)

The effect of the heat transfer coefﬁcient is discussed in the following section.

8.4 Conclusions

Figure 8.17 Transient pattern at t = 60, 300, 780 s, from top to bottom, respectively, all parameters as in Figure 8.16.

8.3.2.3 Simulation Results The formation of temperature and concentration patterns is also observed in the more detailed reactor model, as shown in Figure 8.18. As can be seen, the pattern occurs in a temperature and concentration range that can be obtained in a laboratory reactor. In contrast to the simpliﬁed model, only patterns with decaying amplitude are found. The main reason for this may be that the concentration of the reactant ethane decreases on the sweep gas side along the reactor coordinate but is constant in the simple model. The pattern turns out to be rather sensitive against the heat transfer coefﬁcient. An increase of q˙ reduces the temperature level in the ﬁxed bed, especially in the inlet region, and dampens the temperature oscillations strongly. A decrease of q˙ causes a high temperature peak at the reactor inlet but also reduces the oscillation amplitudes in the rear part of the reactor, as can be seen in Figure 8.19.

8.4 Conclusions

This chapter’s objective has been to provide some insight in the qualitative nonlinear phenomena that may occur in membrane reactors. The two operation

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Figure 8.18

Stationary pattern for the detailed membrane reactor model.

modes of selective product removal and of distributed injection of reactants have been considered. In both cases, different nonlinear effects are predominant. When the membrane is used for withdrawing products, then the main concerns are to achieve high conversion and to obtain the target product with high purity. It turns out that total conversion and simultaneous separation requires a membrane that is only permeable for one product. However, in practice the membrane possesses ﬁnite permeability for all components. Then its beneﬁt for the reactor performance strongly depends on the order of permeability of the membrane for the different components. For the reaction A ↔ B + C the behavior is most interesting when A has lowest or highest permeability, because in these cases there is a certain composition for which the change of concentration through reaction and through mass transfer compensate each other. When A has lowest permeability, this composition gives the maximum product concentration achievable when pure A is fed. When the membrane is used for side injection of reactants to enhance yield, then the stability of the desired solution may become an issue, as shown in the second part of this chapter. Under certain conditions, spatially homogeneous

References

Figure 8.19 Stationary patterns for different heat transfer coefﬁcients: 48, 56, 64 and 72 W m−2 K−1 (from top to bottom, respectively), all other parameters as in Figure 8.18.

solutions give way to concentration and temperature patterns, which may be quite complex. This can be explained by analogy to the dynamic behavior of CSTRs or physically by the charging and discharging of mass and energy storages along the reactor coordinate. Low axial dispersion and a big reactor length support the effect of pattern formation in membrane reactors.

References Benettin, G., Galgani, L., Giogilli, A., and Strelcyn, J.-M. (1980) Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Meccanica, 15, 9. Caracotsios, M., and Stewart, W.E. (1985) Sensitivity analysis of initial value problems with mixed odes and algebraic equations. Comp. Chem. Eng., 9, 359– 365. Fullarton, D., and Schlünder, E.U. (1986) Diffusion distillation – a new separation

process for azeotropic mixtures. 1. Selectivity and transfer efﬁciency. Chem. Eng. Proc., 20, 255–263. Glöckler, B., Kolios, G., and Eigenberger, G. (2003) Analysis of a novel reverse-ﬂow reactor concept for autothermal methane steam reforming. Chem. Eng. Sci., 58, 593–601. Grüner, S., and Kienle, A. (2004) Equilibrium theory and nonlinear waves for reactive distillation columns and chromatographic reactors. Chem. Eng. Sci., 59, 901–918.

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8 Nonlinear Dynamics of Membrane Reactors Grüner, S., Mangold, M., and Kienle, A. (2006) Dynamics of reaction separation processes in the limit of chemical equilibrium. AIChE J., 52 (3), 1010– 1026. Huang, Y.-S., Sundmacher, K., Qi, Z., and Schlünder, E.U. (2004) Residue curve maps of reactive membrane separation. Chem. Eng. Sci., 59, 2863–2879. Hussain, A., Silalahi, S.H.D., and Tsotsas, E. (2004) Heat transfer in tubular, inorganic membranes. Proceedings of the 4th European Thermal Sciences Conference, Birmingham. Kienle, A. (2000) Low-order dynamic models for ideal multiplicity of multicomponent distillation processes using nonlinear wave propagation theory. Chem. Eng. Sci., 55, 1817–1828. Klose, F., Joshi, M., Hamel, C., and Seidel-Morgenstern, A. (2004) Selective oxidation of ethane over a vox/gammaal2o3 catalyst – investigation of the reaction network. Appl. Catal. A, 260, 101–110. Krishna, R., and Wesselingh, J.A. (1997) The Maxwell-Stefan approach to mass transfer. Chem. Eng. Sci., 52, 861–911. Mangold, M., Kienle, A., Mohl, K.D., and Gilles, E.D. (2000) Nonlinear computation in DIVA – methods and applications. Chem. Eng. Sci., 55, 441–454. Mangold, M., Ginkel, M., and Gilles, E.D. (2004) A model library for membrane reactors implemented in the process modelling tool ProMoT. Comput. Chem. Eng., 28 (3), 319–332. Nekhamkina, O., Rubinstein, B.Y., and Sheintuch, M. (2000a) Spatiotemporal patterns in thermokinetic models of cross-ﬂow reactors. AIChE J., 46, 1632–1640. Nekhamkina, O., Nepomnyashchy, A.A., Rubinstein, B.Y., and Sheintuch, M. (2000b) Nonlinear analysis of stationary patterns in convection-reaction-diffusion systems. Phys. Rev. E, 61, 2436–2444.

Nowak, U., and Weimann, L. (1990) A family of newton codes for systems of highly nonlinear equations – algorithm, implementation, application. Technical Report TR 90-10, ZIB, Konrad Zuse Zentrum fur Informationstechnik. Sheintuch, M., and Nekhamkina, O. (2003) Stationary spatially complex solutions in cross-ﬂow reactors with two reactions. AIChE J., 49, 1241–1249. Sheplev, V.S., Treskov, S.A., and Volokitin, E.P. (1998) Dynamics of a stirred tank reactor with ﬁrst-order reaction. Chem. Eng. Sci., 53, 3719–3728. Shimada, I., and Nagashima, T. (1979) A numerical approach to ergodic problem of dissipative dynamical systems. Prog. Theor. Phys., 61, 1605. Travnickova, T., Kohout, M., Schreiber, I., and Kubicek, M. (2004) Effects of convection on spatiotemporal solutions in a model of a cross ﬂow reactor. Proceedings of CHISA 2004. Ung, S., and Doherty, M.F. (1995) Calculation of residue curve maps for mixtures with multiple equilibrium chemical reactions. Ind. Eng. Chem. Res., 34, 3195–3202. Uppal, A., and Ray, W.H. (1974) On the dynamic behavior of continuous stirred tank reactors. Chem. Eng. Sci., 29, 967–985. Wolf, A., Swift, J.B., Swinney, H.L., and Vastano, J.A. (1985) Determining lyapunov exponents from a time-series. Phys. D, 16, 285–317. Yorke, J.A., and Kaplan, J.L. (1979) Chaotic behavior of multidimensional difference equations, in Functional Differential Equations and Approximation of Fixed Points, Vol. 730 of Lecture Notes in Mathematics (eds H.-O. Peitgen and H.-O. Walther), Springer, pp. 228–237. Zhang, F., Mangold, M., and Kienle, A. (2006) Stationary spatially periodic patterns in membrane reactors. Chem. Eng. Sci., 61 (21), 7161–7170.

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9 Comparison of Different Membrane Reactors Frank Klose, Christof Hamel, and Andreas Seidel-Morgenstern

9.1 General Aspects Regarding Membrane Reactors of the Distributor Type

Membrane reactors of the distributor type clearly possess the potential to enhance selectivities and yields in reaction networks. The main reason is based on the fact that a spatially distributed feeding of the reactants can be beneﬁcial. Hereby the speciﬁc reaction rates of the desired and undesired reactions determine the success of the concept. They specify which of the reactants should be introduced in a more concentrated form at the reactor inlets and which reactants should be dosed. The effect of the membrane acting as a distributor is essentially threefold:

• • •

Distributed dosing allows the altering and adjusting of local concentrations. The separated introduction of the reactants causes changes in the local gas velocity proﬁles and, thus, in the residence times. Distributed dosing possesses the potential to smooth the temperature proﬁles and to decrease local heat accumulation and “hot spots”.

All three effects generate differences in overall reactant conversion and product distribution compared to conventional co-feed reactor operation. An important side effect of the differences in the local concentration proﬁles is the fact that in membrane reactors the catalysts applied might be in other states. Thus, an optimized operation of membrane reactors requires the development and application of speciﬁc catalysts. Reactant transfer through the membrane can be realized by convection or diffusion in the case of non-selective porous membranes or by ion conduction or solution mechanisms in the case of dense membranes. The membranes can be catalytically inert or they can be themselves catalytically active. Hereby, the provision of sufﬁcient catalytic functionalities inside the membranes or on the membrane surfaces is not trivial and the application of particulate catalysts, as widely studied in this book, appears to be the alternative which is more easily realized.

Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

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9 Comparison of Different Membrane Reactors

9.2 Oxidative Dehydrogenation of Ethane in Different Types of Membrane Reactors

Ethylene and propylene are the most important building blocks in organic chemistry. Currently they are industrially produced by steam cracking. Ethylene yields in naphta cracking are in the range of 30%. The cracking of ethane leads to yields above 80% and sets currently the standard (e.g., Weissermel and Arpe, 2003). Regarding the yield of the oxidative dehydrogenation of ethane to ethylene there are currently no technologies available which allow competion with the steam cracking of ethane. Focusing essentially on conceptional studies in this book this reaction was investigated as a well manageable model reaction in order to evaluate the potential of membrane reactor concepts. Hereby, initially also the option to remove selectively the formed product ethylene in a membrane reactor of the extractor type was considered (Chapter 1). Since currently no membranes are available which are suitable for the effective selective withdrawal of oleﬁns, this option was not further followed. Oxygen is involved in all main reactions occurring in the network of ethane oxidation. The non-desired deep oxidation reactions are more sensitive to oxygen than the desired oleﬁn formation. This relation in the order of reactions is a general phenomenon in the catalytic oxidation of hydrocarbons over non-noble transition metals and makes axially distributed oxidant dosing meaningful. Thus, it is advantageous to use membranes as an oxidant distributor. Axial oxygen concentration proﬁles are lowered and axial hydrocarbon proﬁles are elevated in membrane reactors in comparison to the joint insertion of reactants in conventional packed-bed reactors. An important aspect regarding membrane reactors is the fact that especially in the inlet sections of the catalyst bed a relative excess of hydrocarbon is present. Thus, it is important to take into account that lowering the oxygen concentration reduces the amount of active vanadium(V) sites on the catalyst and, consequently, the ethane conversion. Contact time prolongation, which is especially pronounced in the packed-bed membrane reactor (PBMR), enhances ethane conversion but lowers ethylene selectivity. Hereby side reactions are typically negative (e.g., oleﬁn pyrolysis yielding soot), but there can be also positive effects (e.g., due to ethane dehydrogenation). Flattening the temperature proﬁles is an important additional beneﬁt of membrane-assisted oxidant dosing. Despite contact time prolongation, the temperature proﬁles in a pilot-scale packed-bed membrane reactor were signiﬁcantly less pronounced than in a reference packed-bed reactor operated with identical overall feed amounts. The reduced hot spots decreased ethane conversion but were found to be beneﬁcial for ethylene selectivity. It was found that all membrane reactor types investigated experimentally demonstrated the beneﬁcial effects mentioned above. However, speciﬁc aspects and differences were also observed.

9.2 Oxidative Dehydrogenation of Ethane in Different Types of Membrane Reactors

9.2.1 Packed-Bed Membrane Reactor

In order to avoid oxygen limitation in the center of the tubular reactor due to the formation of radial concentration proﬁles, the PBMR exploiting ceramic membranes in a dead-end conﬁguration was found to operate most efﬁciently at oxygen to hydrocarbon ratios of unity or slightly above (Chapter 5). To avoid the effect of back-diffusion of products causing a decrease in the reactor performance, high shell to tube side feed ratios should be applied to generate high transmembrane pressure drops. Back-diffusion was observed at low transmembrane pressures differences when sintered metal membranes with larger pores were applied. Furthermore, for the model reaction investigated the PBMR should realize relatively moderate contact times. In comparison to the well established packed-bed reactor (PBR) operation, ethane conversion, ethylene selectivity and ethylene yield were found to be improved in a one-stage membrane reactor and in particular in a three-stage membrane reactor cascade using an increasing oxygen dosing proﬁle (Table 9.1). Furthermore, hot spot formation in the catalyst bed was found to be lower in the PBMR than in the PBR, depending on the operating conditions. The problem of hot spots could be even more overcome by ﬂuidization of the catalyst bed, as applied in the ﬂuidized-bed membrane reactor (FLBMR).

Table 9.1 Performance of different investigated membrane reactor conﬁgurations for the ODH of ethane. T = 600 °C, O2/C2H6 = 1.

Conversion C2H6

Selectivity C2H4

Yield C2H4

Weight of catalyst/ total ﬂow rate

Conﬁguration

(%)

(%)

(%)

(kg s/m3)

PBR (conventional)

55

46

25.6

400

PBMR

50

52

26.2

400

PBMR (three stages; increasing proﬁle)

60

53

31.6

400

FLBMR

43

62

26.7

1750

EMR

46

41

18.9

780

9.2.2 Fluidized-Bed Membrane Reactor

The FLBMR appears to be a promising concept for highly exothermic selective oxidation reactions. Hot spots could be efﬁciently suppressed by means of the excellent heat exchange properties in a ﬂuidized bed. The exploited thermal homogenization by ﬂuidization led to the highest selectivities with respect to

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ethylene observed in all membrane reactors studied (62% vs 52% or 53% for the PBMR, see Chapter 6 and Table 9.1). The ethylene yields for the FLBMR and the PBMR were comparable. However, it should be pointed out that higher W/F ratios are necessary in the FLBMR to realize these yields. Similar to the PBMR, oxygen to hydrocarbon ratios above unity are beneﬁcial for increasing the ethane conversion. A drawback in comparison to the PBMR is the higher space consumption of the FLBMR and the demand for additional optimization of the catalyst particles with respect to ﬂuidization and resistance against higher mechanical stresses. Like in the PBMR, the utilization of sintered metal membranes is possible in the FLBMR. Care must be also taken in order to provide sufﬁcient transmembrane pressure drops to avoid the back-diffusion of ethane and ethylene. 9.2.3 Electrochemical Packed-Bed Membrane Reactor

Selective oxygen transport through membranes by oxide anion conduction is realized in the electrochemical membrane reactor (EMR, Chapter 7). This selective transport avoids in the EMR any dilution of the reactants by inert gases such as nitrogen, in contrast to the reactors which apply non-selective membranes (PBMR, FLBMR). In the case study carried out, the subsequent oxygen transfer from the membrane to the catalyst occured via the gas-phase. In the experiments a direct catalyst re-oxidation by accepting oxide anions from the membrane was found to be unlikely. The EMR reached approximately the 20% level with respect to ethylene yield (Table 9.1), which demonstrates the general feasibility of this concept. Oxygen permeation was identiﬁed to be still limiting, even though oxygen transfer through the membrane was enforced by electrochemical pumping. The rather low oxygen permeability and the high costs of the membranes can be considered currently as a barrier for a successful scale-up of this type of EMR concept. However, if these limitations can be overcome, the EMR concept offers attractive advantages.

9.3 General Conclusions

Membrane reactors of the distributor type possess an attractive potential to enhance selectivities and yields. The potential is highest when there are pronounced differences in the order of reaction between the desired and undesired reactions. Results obtained for the oxidative dehydrogenation of ethane conﬁrmed the general potential of the reactor concept. However, the achieved beneﬁts using vanadium oxide catalysts were not sufﬁcient to pass the threshold for industrial exploitation. For reaction systems in which the local concentrations more strongly inﬂuence the ratio between the desired and undesired reactions, more pronounced improvements can be expected, rendering membrane reactors of the distributor type attractive for commercialization.

Reference

The availability of suitable membranes is another important requirement for successful reactor operation. Hereby a kinetic compatibility between the rates of the reaction and transport processes is essential. This requires a careful selection of the catalysts and membranes. Hereby dead-end conﬁgurations could be used efﬁciently to reduce the need for selective membranes. A general requirement for applications is to avoid the back-transport of products to the feed side. From the results obtained for the oxidative dehydrogenation of ethane, reactors using particulate catalysts and inert membranes could be recommended. This principle can be realized in packed-bed, ﬂuidized-bed and electrochemical packedbed membrane reactors. For highly exothermic reactions in particular the ﬂuidized-bed membrane reactor is attractive. A wider use of catalytic membrane reactors requires several challenging problems in the ﬁelds of catalysis, material science and reaction engineering to be tackled. Important problems that must be solved prior to possible application are also related to reactor safety. The reactor principle allows gases to come into contact via a membrane, while, without the membrane, this would create explosive mixtures. Thus, the possibility of membrane breakage must be considered in the design concepts. With the joint efforts of experts in catalysis, material science and reaction engineering it should be possible to solve the remaining problems, to identify promising reaction systems and to develop successful applications of membrane reactors of the distributor type.

Reference Weissermel, K., and Arpe, H.-J. (2003) Industrial Organic Chemistry, 4th edn, Wiley-VCH Verlag GmbH.

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Index a adsorption 204 – equilibrium constants 73, 79 – irreversible 223 Arrhenius equation 10, 205, 207 asymptotic expansion method 46, 94 atomic absorption spectroscopy (AAS) 69 ATY, see yield azeotropic – binary mixture 241f. – point 244 b Babuska–Brezzi condition 48 back-mixing 16, 133, 167, 174, 183, 186f. batch operation, see process bifurcation 252ff. Brinkman–Forchheimer equation 93, 97 bubble 170ff. bulk ﬂow coefﬁcient 107 Butler–Volmer kinetics 207, 213f.

c capillaries 97f. catalysis – heterogeneous 2, 4, 9, 34, 78, 124, 201ff. – homogeneous 2f., 9, 124 – redox 67 catalyst – anodic (AC) 203 – bed 145f., 150f., 153, 183 – characterization 69ff. – coking 185, 187, 218 – deactivation 185, 218 – layer 43f., 71f., 86, 90, 118, 123ff. – non-reducible oxides 64 – particle size 74, 77f.

– performance 78f. – platinum-based 64 – porosity 32f., 39, 91, 93 – preparation 69ff. – reducible oxides 64 – surface 9, 65, 70f., 74, 129, 170, 184 – vanadia 64ff. catalytic – activity 125, 133, 197, 200 cell voltage 199f. – decomposition 200 charge transfer 200 – coefﬁcients 207 – parameters 206ff. – resistances 200 chemical equilibrium limit 235ff. chemical potential 36f. chemical vapor deposition (CVD) 68 CMR, see reactor co-feed 18 concentration – gradient 117 – molar 9f. – polarization 200 – proﬁle 63, 86, 90f. conductivity – constant 206 – electrolyte 207 – electronic 194, 197 – heat 255 – ionic 194ff. – protonic 219 – solid electrolytes (SE) 197 contact time 63, 144, 150, 152, 156, 175 contactor 4, 7 control–volume technique 47, 49 convection 11, 47, 115ff. convection–diffusion equations 87ff. conversion

Membrane Reactors: Distributing Reactants to Improve Selectivity and Yield. Edited by Andreas Seidel-Morgenstern Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32039-4

270

Index – determing factor 142 – ethane 67, 70, 127f., 141ff. – ethylene 122 – propane 159f. coupling – elements 52f. – faradaic 195, 198, 201 – oxidative methane 217, 221 – thermal 5 current – collector 198, 200 – density 199f., 207, 219f. – efﬁciency 219 – voltage behavior 207f. cyclone 178f.

d Damköhler number 11f., 46, 203 Dankwert’s boundary condition 173 Darcy’s law 33, 40, 138 dead-end conﬁguration 117, 135, 146 desorption 34, 204 dusty gas model, see model differential thermal analysis (DTA) 69 diffuse reﬂection infrared Fourier transform spectroscopy (DRIFTS) 69, 72 diffusion – artiﬁcial term 171 – coefﬁcients 37ff. – conﬁgurational 38 – equimolar 41 – ﬂuxes 36ff. – isobaric 98f., 105ff. – molecular 36, 38ff. – multi-component 174 – resistances 203f. – thermal 42 – transient 98f., 105ff. Dirichlet 87 discretization methods 44 dispersion 106 – axial 137, 171, 174, 203, 236 – coefﬁcients 116, 139, 170f. – heat 252, 256 – radial 137 distillation 2, 241 distributor 4f., 16, 22f., 64, 91 dosing – axial 86 – concept 1, 3, 14f., 133, 159, 176f., 184 – continuous 15, 18 – discrete 15, 17ff. – distributed 13, 140f., 150, 152, 170, 176f. – multi-stage 6

– proﬁle 6, 16f., 94, 134f., 147, 155ff. – stage-wise 15, 17, 134

e effectiveness factor 124, 126f. electrode 187ff. electrolysis 224f. electrolyt, see SE 193ff. electrostatic potential 201, 204f., 214 energy – balance 30, 32, 34, 45, 87 – conservation equation 31, 33f., 45 – efﬁciency 2 – storage 54 enthalpy 30, 237, 251 – formation 34 – reaction 34, 246 – transport 32 equilibrium – chemical 235ff. – limitations 2 – reaction 245f. – vapor–liquid 239, 241 Ergun equation 91 extractor 4f., 16

f Faraday’s law 200f., 204, 219 feed composition 12, 14, 186 feed ﬂow 135f. – rate 151, 153 – ratio TS/SS 135 ﬁnite difference method (FDM) 46, 49 ﬁnite element method (FEM) 46f., 89, 93f. ﬁnite volume method (FVM) 46ff. ﬂow – convective 40, 91, 115, 120, 137, 151, 172 – creeping 38 – density 204 – inversion 109 – laminar 43, 91, 123 – maldistribution 91, 140 – outlet 135 – plug 137f., 203, 254f. – Poiseuille 43, 46 – viscous 38f., 97, 104, 106 ﬂow rate – total 116, 118, 144, 155 – volumetric 9f., 32, 118f., 152 ﬂuid – compressible 89f. – incompressible 46f., 89f., 94

Index ﬂux – density 17, 19f., 173, 196, 251 – diffusive 32, 117, 144 – non-convective 31, 53 – oxygen 195 – total 117, 121 – vector 53 force – friction 33, 93, 140 Fourier’s law 35 fuel cell (FC) 198f., 216ff. – direct methanol (DMFC) 223f. – operating mode 198f., 224, 226f. – polymer electrolyte membrane (PEMFC) 223f. – proton-conducting 221 – solid oxide, see SOFC

g Galerkin least square method (GLS) 47, 87f. galvanostatic control 195 gas chromatography (GC) 64, 74, 147f., 179 – mass-selective detection (MSD) 74, 147f. – thermal conductivity detection (TCD) 74, 98, 147f., 180 gas diffusion electrodes (GDE) 197f. gas dynamic conditions 123 gas hourly space velocity (GHSV) 65, 90, 92, 121ff. gas – phase transport 40 – primary/secondary ﬂow ratio 185fff. – single gas permeation 99ff. genetic algorithm (GA) 111 Graham’s law 41, 104

i ideal gas – lav 106, 172, 104, 251 inf-sup stable ﬁnite element 48, 95f. interaction – gas–wall 39 – molecule–gas 40 interface – membrane/electrode 195ff. – membrane/shell 118 – reactor tube/membrane 117 – support/intermediate 101 – tube/membrane 118f.

k Kaplan–Yorke conjecture 253 kinetic – compatibility 21f. – gas theory 39 kinetic model 63ff. – derivation 73ff. – parameter estimation 19, 79 Kirchhoff’s law 205, 216 Knudsen – diffusion 38ff. – diffusion coefﬁcient 101, 107, 124, 257

l Langmuir–Hinshelwood and Hougen– Watson model (LHHW) 78f., 140, 213, 249 Lattice–Boltzmann method 175 Levenberg–Marquardt algorithm 79 local deterministic optimizer (LD) 111 local projection (LPS) 48f., 51, 88f. Lyapunov exponents 253

m h Hagen–Poiseuille law 40 heat – capacity 34, 236 – conduction 35 – ﬂux 5, 35, 237, 245 heat transfer 2, 29, 32, 35, 97, 123, 139, 151, 167 hydrogen – pumping 220f., 226 – sensor 220f. – transfer 219 hydrogenation – high-temperature 226 – partial 13, 133, 226 – selective 8, 13, 22, 226

Mach number 35 Mars–van Krevelen mechanism 78f., 140, 209f., 213, 249 mass balance – component 138 – equation 11, 13, 17, 45 – PFTR 10ff. mass – ﬂow rate 43, 116, 172 – fractions 43, 116 – loss 86 – storage 54 mass transfer 21, 29, 32, 97 – coefﬁcients 106, 172 – convective 172f. – limitations 77, 125f., 174

67, 69,

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272

Index – radial 116 – rate 184 – resistance 120, 200 McCabe–Thiele diagram 238, 242 membrane – asymmetric 97, 146 – catalytically active 7 – ceramic 6f., 22, 97, 101f., 113f., 145, 153f. – composite 7, 54f., 101, 103ff. – defects 107 – dense 6f., 194f. – homogeneous 105, 107f., 143 – metallic 97, 107ff. – multilayer 97f., 109f., 113 – organic 6f., 195, 222ff. – oxygen ion-conducting inorganic 193 – polymer electrolyte (PEM) 222ff. – porous 6f., 30, 32, 97, 105, 145f., 194f. – single-tubular 134 – sintered-metal 153ff. – structure 98, 107ff. – surface chemistry 7 – thickness 107f., 116, 119, 144, 202 – tortuosity 39, 98, 107, 119 mixed ion/electron conductors (MIEC) 194f., 228 model – continuum 29 – 1-D 203f. – 1-D + 1-D 42, 137f., 203 – 1-D PBMR 42, 136, 141ff. – 2-D CMR 42, 120 – 2-D PBMR 42, 139f., 152f. – 2-D PBR 152f. – discrete 29, 96f. – discrimination 73, 79, 81 – dusty gas model (DGM) 40f., 55, 86, 97f, 100, 105ff. – electrochemical 205 – extended Fick model (EFM) 137 – heterogeneous two-phase 170 – mechanistic 73 – multi-dimensional 42 – nonisothermal 55, 89, 245ff. – single-layer 55f., 107ff. – two-layer 110ff. – two-phase ﬂuidized-bed 171ff. – validation 97ff. momentum conservation equations 31, 33f., 44, 80 momentum transport equations 30ff. multi-level multi-discretization solver 49

n Navier–Stokes 47 30, 45f., 48f., 89, 94, 97 Nernst’s law 198 network theory 52f. Neumann outﬂow 87 Newton iterations 139, 173 Newton’s law of viscosity 35 non-electrochemical modiﬁcation of catalyst activity effect (NEMCA) 200 nuclear magnetic resonance (NMR) 69 Nusselt number 42

o ohmic resistances 200, 207 Ohm’s law 204 open-circuit cell voltage (OCV) 198ff. overpotential 205 oxidation – cross-over 223 – direct 223 – electrocatalytic 218 – partial (POX) 8, 13, 16, 22, 133f., 168, 196, 201f., 208, 218 – selective 8, 13, 63f., 202 – total 16, 201 oxidative coupling of methane 217f. oxidative dehydrogenation of butane (ODHB) 134, 168 oxidative dehydrogenation of ethane (ODHE) 63f., 140f., 153ff. – electrochemically supported 213f. oxidative dehydrogenation of propane (ODHP) 63f., 140, 158ff. oxygen – concentration proﬁles 135f., 142, 152, 176f., 181ff. – deﬁciency 219 – excess 71f., 148f., 158f., 187 – lattice 210, 213 – lean 71f., 129, 150, 152, 158 – pumping 208, 213, 218 oxygen ion conductors 193ff. – high-temperature 193, 196, 216ff. – low-temperature 196

p pattern – formation 248ff. – spatial 250 – stationary 250, 255ff. – transient 259 PBMR, see reactor PBR, see reactor Péclet number 46

Index permeability – coefﬁcients 91 – constant 101, 124 – oxygen 194, 196 permeate ﬂux 101, 107, 109 permeation – experiments 111ff. Petrov–Galerkin – pressure-stabilized approach (PSPG) 49 – streamline upwind method (SUPG) 47f., 87ff. PFTR, see reactor pilot scale 22, 64, 134, 145f., 178 potentiostatic control 195, 198 pressure – drop 43, 86, 90, 109, 115, 120f., 144, 153f., 167 – gradients 91, 101, 138 – partial 39, 75, 150 – total 40, 55, 101, 236 – transmembrane 89f. process simulation tools, 139 – DIANA 51, 111 – DIVA 51, 81, 252 – COMSOL 139, 173 – FLUENT 49f., 114 – MATLAB 49, 51, 137 – MooNMD 49f., 93 – Newton method NLEQ1S 254 – ProMot 49, 51ff. – UMFPACK 139, 173 proton ion conductors 193ff. – high-temperature 193, 219f., 222 – low-temperature 222ff. – perovskite-type oxides 219, 222 protonic defects 219

– networks 1f., 5, 10, 12f., 15f., 22, 63ff. – rate constants 14, 18, 73 – redox catalysis 67, 140 – reversible 2, 5, 241 – second-order 11f. – unselective 201 – water gas shift 141, 221 – zone 5, 21, 135, 145, 168, 201 reactor – autothermal 2, 168 – catalytic membrane (CMR) 6, 42f., 85f., 115, 120ff. – cylindrical tubular 21 – ﬁxed-bed 3f., 18, 134ff. – ﬂuidized-bed (FLBR) 167ff. – ﬂuidized-bed membrane (FLBMR) 167ff. – multi-stage membrane 136ff. – packed-bed membrane (PBMR) 6, 30, 42, 85f., 133ff. – packed-bed membrane reactor cascade (PBMR-3) 134ff. – packed-bed (PBR) 3ff. – plug ﬂow tubular (PFTR) 10f., 13f., 16, 137 – proton exchange membrane (PEM) 224ff. – single-stage membrane 136ff. – sintered metal packed-bed membrane (PBMR-SM) 153f. – solid electrolyte membrane (SEMR) 193ff. – start-up 113, 239 – temperature proﬁle 90f., 133, 135, 150f., 254 – tubular 3f., 13ff. reforming 168, 218 residence time 5, 11, 106, 119ff. Reynold’s number 46f., 93f., 96

q quasi-homogeneous phase 32 quasi stationary 247f., 251

r reaction – biomolecular 12 – Boudouard 65 – charge transfer 200, 206ff. – conversion 2, 5, 9f., 12, 14 – electrocatalytic membrane 221f. – electrochemical charge transfer 201ff. – endothermal 2, 5 – exothermal 1, 5, 167, 248, 252 – ﬁrst-order 11f., 210, 248 – gas–liquid 4 – inhibition 86

s SE (solid electrolyt) 193ff. selectivity – differential local 15f., 156 – enhancement 5 – ethylene 76f., 117, 122, 140ff. – integral 13 – intermediate products 133 – propylene 159f. sequential quadratic programming (SQP) 17 shear stress 35 Sherwood number 42 shock-capturing term 89 sieving effect 38f. simulation, see process simulation tools

273

274

Index slip boundary condition 46 SOFC (solid oxide fuel cell) 207, 216ff. – high-temperature 216 – intermediate temperature 217 solid electrode membrane reactor, see reactor species balance 30f., 87 SS/TS (shell-side/tube-side) ratio 118ff. steady-state condition 10, 43, 99, 114, 137f., 170, 252ff. – quasi- 204, 209f. Stefan–Maxwell equations 36, 40 storage – capacity 250f. – element 53 streamline upwind Petrov–Galerkin method (SUPG), see Petrov–Galerkin structure–activity relations 66ff. STY, see yield support – α-Al2O3 support 65ff. – pore diameter 119f. – silica 68f. – thickness 118ff. – titania 68f. – zeolites 68 – zirconia 68 suspension phase 170ff. sweep gas side 5, 246, 256, 258 syngas 217

t temperature-programmed desorption (TPD) 69 temperature-programmed oxidation (TPO) 69 temperature-programmed reduction (TPR) 69, 71f. thermal – capacity 237 – conductivity 35, 43, 87 – dehydrogenation 141 – equation of state 237 – equilibrium 34 – gravimetry (TG) 69 – resistance 123 – stability 6 thermodynamics – irreversible 36, 52 Thiele modulus 203 transition metal oxides 64, 66 transmembrane – mass transport 115 – pressure difference 89f., 126f., 144, 153f.

transmission electron microscopy (TEM) 73 transport – coefﬁcient 30, 43, 86, 97 – convective 31, 52, 86 – diffusive 86 – equation for species 31, 33f. – kinetics 35ff. – resistances 123 – viscous 33 tunneling effect 93 turnover frequencies (TOF) 71f. turnover number 43

u upwind approach 87f. user-deﬁned functions (UDF)

50f.

v velocity – axial 116 – component 36 – cross-sectional 91 – ﬁeld 45, 86f., 89, 91, 115 – gradients 35 – interstitial 32f. – mass-average 36, 38 – proﬁle 46, 85f., 90ff. – radial 44 – species 32 – superﬁcial gas 32f., 91, 138, 172, 181, 184f. – vector 44 viscosity – dilatational 35 – dynamic gas 104 – tensor 32 viscous slip 43

w washer 178f. Wicke–Kallenbach cell

98

x X-ray diffraction (XRD) 69 X-ray photoelectron spectroscopy (XPS) 69, 71

y yield 2, 8, 12ff. – area time (ATY) 21f. – ethylene 117, 122, 127f., 141f., 214 – intermediate products 133 – propylene 158 – space time (STY) 21f.